Let the yard dry out for a day or two until it is moist but not saturated. If the soil sticks to your shoes, it is too wet.
Mark the areas where with sprinkler heads, cables, underground wires, pipes and septic lines. Avoid these areas.
Make a pass across your lawn with the aerator in a similar manner as you would when mowing your lawn. Many of the rented machines are push aerators. Some however, attach to the back of a riding mower.
Make three to four more passes with the aerator, each time switching the row direction. For example, push the aerator in a south-north direction the first time, then in a east-west direction the second time. Go back to the south-north direction for the third pass and so forth. If you are reseeding after aerating your lawn, make a total of 10 passes.
Rake the lawn to break up the clumps of soil and remove any thatch. It is now ready to reseed, if applicable.