Q: I got the following from my lawn company when I asked about aeration.

We provide core aeration but do not offer the Criss-cross method. We have found this to cause too many divots in the lawn from the tires (from repeated 180 degree turns with the equipment). We prefer to use the circular method which causes very few divots from turns and gets equally good results. Also, if the lawn is sufficiently moist for good aeration, the secondary passes will actually mash the previous holes closed. For these reasons most companies don’t really use this method. If you insist on this method, aerators can be rented from most rental companies for about $60 per day, some mowers may be willing to do this for you as well.

A: For lawn aeration, I took this

Penetration depth depends on soil type, soil moisture, tine diameter, and the weight and power of the aerifier. Soil cores should be left on the lawn to be broken up by rainfall and traffic. If their appearance bothers you, you can speed up their disappearance by raking them into the grass. Whichever machine you use, go over the lawn twice, once in one direction, and then in a perpendicular direction for best results.

from Aerating Lawns

I got this

Remove soil cores that are one-half to five-eighths of an inch in diameter and 3 inches long. For best results, aerate lawns when the soil is moist. Avoid aeration when soils are dry or excessively wet. The tubes or tines will not be able to penetrate deeply when the soil is dry. The tubes or tines may get plugged with soil when the soil is wet. Lawns that are properly aerated should have 20 to 40 holes per square foot. Since most aeration machines won’t remove the proper number of holes with a single pass, several passes are often necessary. After aeration, drag the lawn to break up the soil cores on the soil surface.

from Home Lawn Aeration

Personally, I think 10-12 holes per square foot would suffice for adequate lawn aeration.