Question
I have a large area that is partially under trees and I would like to know how to seed it. I live in connecticut.

Answer
Good Evening Bob:
The best time to seed a lawn in your area is late August to early October. The second best time is now.  The reason late summer is best is because the new seedlings will be going into the cool part of the year rather than the hotter part. This will keep the seedlings from being over stressed.
As long as your lawn receives adequate sun it will survive nicely. The area under trees is another story.
Lawns in the shade are typically thin, weak, and of poor quality. Maintaining a quality stand of grass in the shade can be difficult and requires modifications in lawn care practices. Shade-tolerant grasses still need an acceptable amount of light to grow. In addition, lawns in shade areas generally do not have the ability to tolerate or recover from stress problems as compared to lawns growing in full sun.
Choosing a shade-tolerant grass mixture is critical.
Kentucky bluegrass generally does poorly in the shade, but some of the more shade tolerant cultivars include Bensun, Bristol, Eclipse, Glade, Nugget, Touchdown, and Victa.
Care of lawns in shade areas are different than lawns located in full sun. Mow at 3 inches (7.62 cm), and fertilize less in the shade, as too much nitrogen can be detrimental to shade lawn species. About 1 to 2 pounds of actual nitrogen per 1,000 square feet per growing season is all that is needed. When watering shade lawns, do so as infrequently as possible, and water deeply. Reduce traffic over lawns in the shade.
If these practices have been followed but the lawn still fails, there probably is not enough light even for a shade-tolerant grass species. Often a shade lawn mix is seeded, comes up fine, but declines rapidly due to a lack of sufficient light.
Recommended seed mixtures for shade
Light to moderately shady, dry areas
30 percent to 50 percent Kentucky bluegrass plus 50 percent to 70 percent fine fescue (blend two or three varieties of each species and mix). Use 3 to 4 pounds of seed per 1,000 square feet.
or
100 percent turf-type tall fescue (blend two or three varieties). Use 5 to 7 pounds of seed per 1,000 square feet.

Moderately shaded, dry areas
100 percent fine fescue (blend two or three varieties within a species or mix two or three species). Use 3 to 5 pounds of seed per 1,000 square feet.
or
100 percent turf-type tall fescue (blend two or three varieties). Use 5 to 7 pounds of seed per 1,000 square feet.

Shady, wet areas
50 percent to 70 percent or more rough stalk bluegrass plus 30 percent to 50 percent perennial ryegrass (a blend of two or more varieties). Use 3 to 4 pounds of seed per 1,000 square feet.

If lawn grasses have continued to fail, try a shade-tolerant groundcover or mulch, possibly in combination with ferns or woodland flowers.

Steps for new lawn establishment in sunny areas:
Step #1. Get A Soil Test.
Testing the soil is the best way to determine the nutrients your soil may be lacking and the amounts required to provide the best start for your new lawn. A soil test will also indicated the soil pH (acidity or alkalinity) that may need to be adjusted. Soil testing information and services are available through private testing companies or your County Extension office. When you send your soil sample in to be tested, request that the testing service provide you with fertilizer and other amendment recommendations for your lawn.
To take a soil sample for testing use a spade, trowel or bulb planter to remove a plug of soil six inches deep. Obtain similar cores from other random locations in the area of your future lawn. Do not take samples were fertilizer, manure or other chemicals may have been applied. Mix the soil thoroughly in a clean pail. Remove about a half pint of the well mixed soil and let it dry at room temperature. Remove debris such as leaves, vegetation, sticks and large stones. Fill the soil test container to the amount required. Either mail or deliver to the soil test facility.   

Step #2. Get Rid Of  The Weeds.
Most annual weeds will be eliminated by tilling the soil. Perennial weeds, and other perennial grasses are more difficult to get rid of  because they can re-grow after tilling. Applying a nonselective-herbicide (such as Round-Up) when the weeds are actively growing will eliminate perennial weeds. After the application you must wait 10 to14 days before tilling the soil.  I cannot stress enough, as with any herbicide, read and carefully follow all label instructions.

Step #3. Prepare the Soil for Tilling.
The soil test results will indicate the fertilizer analysis needed and at what rate. Apply those materials recommended for adjusting the soil pH at this time also. Choose a fertilizer with the proper ratio of each of the nutrients to correspond to the soil test results. The fertilizer label must state the percentage by weight of nitrogen, phosphorus and potassium in that order. A 20-10-10 fertilizer has the mineral elements in the ratio of two parts of nitrogen, one part of phosphorus and one part of potassium (2-1-1), as does a 10-5-5. The difference is that weight for weight the 10-5-5 contains half as much fertilizer value as the 20-10-10, and twice as much would have to be used for the same results.                                                                                                A 100-pound bag of 10-5-5 fertilizer contains 10 pounds of actual nitrogen (100 lb x 10 percent nitrogen = 10 lb), five pounds of actual phosphorus (100 lb x 5 percent phosphorus = 5 lb), and five pounds of actual potassium (100 lb x 5 percent potassium = 5 lb). The remaining 80 lb (100 lb minus 20 lb. = 80 lb)is a filler that makes spreading the fertilizer easier and at the proper rate. The amount of nutrients in any other fertilizer can be determined in the same way. The amount of fertilizer product to apply is based on the percentage of nitrogen, the first number in the analysis.
If a soil test was not conducted, a fertilizer high in phosphorus should be initially applied at a rate of 2-3 lbs. per 1,000-sq. ft. The fertilizer label must state the percentage by weight of nitrogen, phosphorus and potassium in that order. A good starter fertilizer would have N (nitrogen), P (phosphorus), and K (potassium) at a ratio of 4-5-1 such as 20-25-5.

Step #4. Till the Soil.
Tilling the soil works the  fertilizer and other amendments into the soil. It helps the new grass
seed take root in the soil and it makes the soil easier to smooth out. Remove all debris such as large stones, tree roots and most importantly discarded construction materials. The soil should then be tilled to a depth of 4-6 inches.

Step #5. Raking
Using a garden rake remove any rocks and debris that has been brought to the soil surface. Fill in the depressions and level the ground as best as you can. Leave the soil at least ?inch below the surface of patios, walks and driveways. With a roller no more than half full, roll the area in two different directions. Rentals of lawn rollers are available at most rental supply stores.
After rolling, rake a second time to even the soil. Water the area thoroughly, allowing the soil to settle. When the surface has dried and can be walked on, rake the area a third time filling in low areas and loosening the surface.

Step #6. Seed the Area
Don't skimp on the price of seed. Select the best quality seed available using improved varieties, mixtures or blends recommended for your area by your local nursery or your County Extension Office. Only a small percentage of non-perennial grasses should be present and no noxious weeds should be named on the label.
Using the recommended pounds per 1,000 sq. ft., sow the seed with a drop or rotary spreader uniformly across the tilled and raked area (rotary spreaders allow for quicker and more even seed distribution). Use half the amount in each of two different directions (at right angles) to help ensure good coverage. When distribution of the seed is completed, lightly rake the seed into the soil (Do not rake more than ?inch deep). Next, use an empty roller to firm the soil surface.

Step #7 Watering.
It is very important that a newly seeded lawn be kept moist at all times but not saturated! After the seeds have germinated and have begun to establish a root system, reduce the frequency of watering. Too much water will inhibit germination and promote disease. As you reduce the watering frequency you should also increase the amount of water applied each time. After 6 to 8 weeks water as an established lawn.
Deep, infrequent watering is best for most established lawns. Water until the soil is  soaked to a depth of 4-6 inches, which allows the water to reach deep into the root system. Usually this will amount to about one inch of water per week. Set out a series straight sided containers under your sprinkler system (Tuna cans, Cake pans etc.). Time how long it takes until the one inch level is achieved. You can then use this time figure for future watering without using the cans.
Watch for runoff during the watering period. It is possible that your lawn will not be able to soak up the water as fast as your sprinkler is putting it down. If this occurs shut off the sprinkler for an hour and then turn it on again.
The best times to water your lawn is in the early morning or early evening when there is generally less wind and heat. Do not water in the heat of the afternoon, when water evaporates too quickly and very late in the evening, which can cause the lawn to stay wet all night. This may encourage disease development. Shaded turf requires less water than lawns in full sun. The best schedules are those determined by observing the appearance of your lawn.  Turf that is moisture deficient will not spring back up after walking on it.

Mowing:
Make sure that your lawn mower has a newly sharpened blade. You can sharpen a lawn mower blade at home by simply using a grinding stone or file. Some mower stores and rentals that provide sales & service will sharpen your mower blade for a nominal fee. If you sharpen your own blade make sure it is equally balanced. Use a small nail and place it through the center hole of the blade. Let the blade balance itself on the nail. If one side of the blade falls below the center remove more material from the opposite side of center until balance is maintained.
Proper mowing will increase your lawn's density, attractiveness and reduce lawn care problems. Cool season grasses such as bluegrass, ryegrass and fescues may be mowed with either a rotary or reel mower. Adjust the mower to the recommended height for your grass seed variety.
Bluegrass, Perennial Ryegrass, Tall Fescue, and Fine Fescue should be cut in a range of 2 to 3 inches.
Increase the mowing height ?inch (from the maximum figure above) for shady areas, immediately following a drought period or when insect injury or high traffic has weakened the grass.
It is important to mow on a regular schedule and avoid removing more than 1/3 of the top growth. That is the key to a dense and healthy lawn.

If you mow on a frequent regular schedule you may leave the clippings if desired. Clippings decompose quickly and help put nutrients back in the soil. During times of rapid growth or when more than 1/3 of the top growth is removed, clippings are best removed.

Fertilizing
A fertilizer with N (nitrogen), P (phosphorus) and K (potassium) analysis ratios of 3-1-2 or 4-1-2 are acceptable for use on any lawn. Examples on the fertilizer bag that fit these ratios are 12-4-8, 21-7-14, 16-4-8 and 20-5-10. The fertilizer should also have at least 1/2 of its nitrogen (N) in a slow soluble/slow-release form.
Lawns fertilized with these forms of nitrogen (N) will have better color, thickness and reduced leaf growth.
Fertilizer application rates should be as low as possible and still produce a high quality lawn. If the amount of nitrogen (N) - (the first number of the analysis listed on the bag) is between 5 and 12, than the application rate should be 10 lbs. for every 1,000-sq. ft. of lawn. If the number is between 12 and 18 the application rate should be 6 lbs. per 1,000 sq. ft. Anything over 19 should be applied at 4-5 lbs. per 1,000-sq. ft. of lawn. These ratios are guidelines only. Always apply the fertilizer at the recommended rate listed on the bag.
The best time to fertilize your lawn is when it is actively growing and in need of nutrients.
Begin your fertilizer program as the lawn begins to grow and green-up in the spring, then reduce applications as the weather gets hotter. When the cool weather returns in the fall, the lawn can again be fertilized. A late fall application, after the first frost, will increase lawn quality the following spring.

Once again, leaving your clippings on the lawn, you are fertilizing the lawn almost on a continuous basis, possibly extending the time period between commercially manufactured fertilizer applications. Lawn fertilization is good, but a lot at one time may cause problems.

Weed Control
A certain amount of weeds are inevitable with a new lawn. Hand weeding a new lawn after the first mowing is best. With large lawns the use of herbicides may be the best solution. Check with your County Extension Office and ask for recommendations. Remember to follow all label instructions for applications and apply only to a lawn that is healthy and actively growing.

I have given you a couple of web sites that will pertain to your area.  I could not find one for Connecticut.

Copy and Paste to your browser then hit "Go"

Establishing a home lawn (Maine)
http://www.umext.maine.edu/onlinepubs/htmpubs/2367.htm

Starting and overseeding new lawns (New Hampshire)
http://www.ceinfo.unh.edu/Pubs/HGPubs/startosl.pdf

Have a good lawn!
Floyd McMahon