Seeding a ruined lawn

I just moved into a house where half of the front lawn has been destroyed by vehicles parking on it. I would like to seed this area and make it look better. But I have never done this before. I would like the proper steps (procedure) for seeding a lawn.
There is a pecan tree that has shed its leaves for many years without proper raking. So it has composted over time to the point of raising the elevation of the lawn. Due to this the topsoil is very rich and fertile.
Also, I would like to know which kind of grass would grow best in full shade for half of the day and full sun the rest of the day.
Any help would be appreciated.
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StevenP wrote:

Since the soil is of good quality, but has had vehicles parked on it, I would first use a core aerator, which you can rent. Then I'd fill in or regrade any low spots. Then, I'd use a slice seeder/over seeder, to apply the seed. Apply starter fertilizer. Also, before you start, test the soil PH and adjust if needed by applying pellitized limestone. You can rent these machines for about $45 a half day.
Since I live up north, and it sounds like you live in the south, someone else will have to give advice on grass type.
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