The most accepted pratice is to Aerate first making as many holes as you can. 3 to 4 passes or as many as you think is needed. This will not only loosed up the soil but will also expose soil and bring some to the top as cores. let them dry a bit so they will break up, then proceed to oveseed with a slicing seeder with fixed knife blades. Some will even spread the seed first and then go over the area with a vert-i-cut machine to slice in the seed. Eith way you will be breaking up the cores, pulling up thatch / while making slices down to and into the soil and stirring the seed up into the thatch you have just pulled up. When you are done water and the water will wash the seeds and dirt out of the canopy you have made and into the low spots on the lawn. This would be the aeration holes, the slits made by the overseeder and other low spots that have no grass growing. After-care is the most important part. If the homeowner does not follow through with a good watering program all your work could go to waste.