First of all, save yourself some time and/or money. Make sure that aeration is needed before you hire someone in or go rent an aerator. The easiest way to check for soil compaction (and, therefore, the need for core aeration) is to take a medium size screwdriver out to a few different areas in your lawn. Try pushing the screwdriver into the ground up to the handle. If this can be done without much pressure, you probably don't need to aerate.

If you find that lawn aeration is necessary, core aeration is the best method. Spike aeration can be helpful, but tends to be a more temporary method. Slitting is ok too. It has the side benefit of dethatching the lawn as well. However, keep in mind that slitting also causes a certain amount of stress to a lawn by ripping through the sod. It's not likely to kill the lawn, but the less stress, the better. I suggest if you want to aerate and dethatch use a core aerator and then apply a good liquid organic dethatching solution. The core aeration helps the solution to penetrate better so that it is even more effective.

Core aeration can also be helpful before topdressing a lawn. When topdressing, the main objective is to get a good topsoil (or maybe some compost or sand) mixed into the soil so as to break things up and possibly provide some of the beneficial nutrients and organisms which the soil may be lacking. In light of this, it seems obvious that aerating beforehand will provide much better conditions for this mixing to take place since there will be holes for the topdressing material to drop into. In this case, as well as when compaction is severe, it may be beneficial to aerate in two directions (perpendicular to one another).