My lawn is in desperate need of overseeding and fertilizing.

Thatch the lawn, rake the weeds and dead grass out, apply a few inches of topsoil, lime,grass seed for your location,starter fertilizer and top with peat moss.Keep moist until the seed germinates.

Here are some good articles on this:

https://yardcare.toro.com/restore/restoring-a-tired-lawn/eight-steps-to-restoring-your-lawn/

http://homeguides.sfgate.com/reseed-lawn-weeds-46229.html

http://www.landscape-america.com/lawns/lawncare/seeding/revival.html

Here is an article that might help - https://www.lawn-care-academy.com/overseeding-lawns.html

A soil test is always recommended before chemical applications according to my master gardeners class for healthy turf.

Sorry I realized I sent you the wrong article at first, I edited it above. Here is one on starter fertilizer - https://growgreenfood.com/best-fertilizer-for-grass

I would first dethatch the lawn using a rental machine, or buy the blade for your mower. Then rent the lawn aerator to improve drainage. Then reseed and water a lot.