You can aerate in spring or fall. The limiting factor is the hardness of the soil as most rental aerators are not very heavy so will not penetrate well in hard soil. Also, if the soil is too wet, the aerators will not pull a core so you need damp soil that is not too wet.

Spring is a great time because grasses produce new root systems in the spring and thus the aerification holes create channels for the roots to grow deeper. We have done research showing that simply by aerating your lawn, you can use 20 - 30% less water.