Question
Thanks for your response.  I have had the plant about 4 months.  Most of the browning is on the bottom and middle leaves; are getting new growth at the top.

I water about once a week - don't have a watering system (?).  Have never fertilized.  

Beyond how to prevent further browning, what is the proper way to handle the brown leaves - pull them off, but off the tips, or just leave them?  Would appreciate further advice.  Thanks, cj

Answer
You're saying the damaged leaves are NOT the youngest ones, but the older and middle leaves?  Overwatering symptoms include Dark Brown patches, Yellowing, curling and/or dropping leaves on a Dracaena.  My money's on the way you are watering -- which is PROBABLY too much.  Drench the soil in the pot, and let it run out.  Then let it sit there to absorb the water left in the underdish.  Empty the underdish after 30 minutes to keep the plant from sitting in the water.

Dark Brown tips and margins may also be a reaction to Fluoride in your local water supply.  Dracaenas are sensitive to this chemical.  Make sure the pH of the water is slightly acidic -- start using rainwater or bottled water if you have a heavily fluoridcated water system and add a DASH ONLY of Vinegar per gallon of this pure water.  Also try to keep your Dracaena protected from cool temperatures -- this is a tropical plant that does not like cold air, which includes any temps lower than 50 degrees F.

When watering, make sure that weekly drink is a deep, long soak from underneath.  After a half hour, make sure the water underdish is removed so that the plant is not sitting in water for long periods of time.  Dracaena leaves tend to get Brown when soil is excessively wet or dry.

Just to cover all the bases here, you should know that direct Sun can also cause problems -- leaves sunburn (center Browning) from too much UV; if you are growing this outdoors or in a Southern Window, see what you can do to tone down the light, although from your description I am inclined to feel this is not the case here.  Besides, Brown tips and/or edges can also be caused by TOO LITTLE Sun.

The Brown leaves are unsightly and many people remove them or slice off the Brown edges and save the rest of the leaf.

Bottom line, though, is this:  new growth that you're seeing indicates this plant is not so bad off at all.  You just need a little more time with it.  After one year, you'll have it down.  Keep a good thing going.  And remember, this is a beautifully fragrant plant when mature.  Many people never find that out.