I am having 18 pine trees removed from my yard (Wisconsin). The area under the trees is nothing but dirt. What will I need to do to repair my lawn?

Pine trees grow well in acid soil. Get a soil test done, you will need to add lime to this area and mix it into the top few inches of soil before seeding grass there. If there are fresh pine needles there rake those off, don't worry about the decayed ones. Consider having the trees cut down leaving stumps, you could quickly grow a second crop of Chistmas trees from the stumps in like 3 or 4 years and sell them for cash while waiting for your lawn to thicken up...