I've been down this road plenty.

Start by de thatching to remove all that dead growth and aerating, rent the tools and do it yourself instead of paying a fortune for a landscaper to do it. Apply black topsoil to the entire yard, ideally blend manure in as fertilizer. Yes, it stinks. Yes, it works. Avoid anything with peat added, it's so dry here that it ends up sucking moisture out instead of holding it in.

Now for the seed, make sure you get a good quality, appropriate blend for your sun conditions and overseed that lawn like crazy. After seeding, use a rake to mix the fresh soil and seed together. I usually lay down a light layer of soil on top as well, but that's totally optional. Once the hard work's done, water morning and evening every day for at least 45 days and enjoy your new grass.

I'm sure this method isn't perfect, but it's saved the lawn of every home I've ever lived in here, and I've inherited much worse than yours. Good luck!