Always start with a lot of thought before action...is saves a ton of time and energy and money.
WHY is the first question. Why are there so many dead spots? We can't see all the tree tops so we don't know if shade is causing this, compacted soil or perhaps low spots on the turf, even the wrong seed potentially. But lotsagrass has the right idea and I'll share my thoughts also. BUT...until you answer why, don't move forward.
1) After figuring out why there are dead spots, you need to mow low (1" approx) and remove as much thatch as possible. Extremely tiring by hand with a metal rake, but cheapest solution. Renting a dethatcher or hiring someone to do it is a good idea if possible, unless you are young or want to really build up a huge sweat. Thatch must be removed from the lawn.
2) Aerate. Absolutely. If you want to overseed it will help with any possible compaction issues and also helps create a healthy lawn in any event. Plugs sit exactly where they were pulled from, they decompose and disappear into the soil in a few weeks.
1a/2a) You can easily hire someone to do both services and with their pro equipment the cost will probably be worth it.
3) Overseed. Slit seeding is superior (can hire for this or do yourself), but even broadcast seeding is just fine which is fast and cheap.
3a) BUY GOOD SEED. REPEAT! BUY GOOD SEED. Most likely a mix of bluegrasses mixed with a fescue mix, depends mostly upon how much sun it gets. Full sun can be all bluegrass, some shade = some fescue, lots of shade = 50/50 mix imo.
4) TOPDRESS. Peat moss mixed with topsoil is a great mix, thinly applied. No more than 1/4 to 1/2" when putting over seed. This will help retain moisture, protect the seed, and provide some nutrients for the overall lawn health. Peat moss has the added benefit of making it easy to see when the area dries out (light brown = dry, dark = moist/wet). Read up online about topdressing. It's labor intensive and worth every minute of the work. Short version: mix the topdress, shovel in small piles across the lawn and spread it with the back of a metal rake. TIRING!
5) Water properly. Keep it constantly moist, not soaked, not dry.
1a-5a) Remember you can hire someone to do all this and do it relatively cheaply. That is what this site is about, pros who know their stuff, have the equipment and will do it right.
My view is this -- I love this stuff and do it myself purely because I love it. But pros are better at it, and if what you want is a beautiful lawn and to maintain it yourself (mow, fertilize, water) don't be ashamed to shell out some bucks for someone to do this for you...because in the end you'll have a beautiful lawn.
A pro can and will do it all in one day for you. I am not a pro, and don't know or recommend particular ones but all you have to do is ask...start a new thread asking for someone in your area to come over and give you a quote. They are experts at identifying WHY you have a problem too, which may be key here. So if you want to do it yourself, I think the steps I outlined above will get you a great result, but a pro is faster and has better equipment and therefore may be cost effective for you.