This will be the first Spring that we will have a backyard, but we have no idea what special treatments (if any) our lawn needs in the Spring.
Also, if it does need a special treatment, can you do it yourself or do you have to hire a company to do it?

First of all, rake the backyard with a grass rake to get up most of the dead grass, foliage and the small branches.Then you can overseed with the same strain of grass as the back, fertilize as recommended by the maker of the fertilizer you are using and water frequently for the first couple of days. This will set the seed, get some fertilizer into the ground to promote spring growth. You can do it yourself or have a service do it which could be costly.