One of my homes had dense shade and big trees in the back yard that made it almost impossible to keep grass during the summer, so every spring I had to replant. Finally cut down all the trees and have an actual lawn for a change. It's not just the shade that kills grass, it's the large tree's root network sucking all the moisture and nutrients out of the soil so the grass struggles and finally dies. Especially if you have a dry summer.
I'm not a guru, but my experience is that you need decent top soil, or at least loose soil that grass can grow in. Rake it and then spread the seed. Rake it again covering the seed slightly. Some people drop Straw on it to protect the seeds and keep in moisture but I have never done that. I just raked. It needs to be kept moist for a week or two until it sprouts and grows to about an inch, then you can cut back on the water a bit. Try and avoid puddling as that will ruin the areas that get the puddles. Hopefully you don't have flocks of birds that will scratch for the seeds.
I have had great success with "Miracle Grow" Spray for lawns. This gives the seedlings a good shot of the proper nitrogen to get them going. You just buy the spray bottle and dump in the blue granules of lawn food. Attach to a hose and spray away.
I have had professional landscape guys try and put in a lawn in my wooded back yard and their method of spreading a lot of straw and dumping a ton of top soil didn't work any better than me just raking, seeding, raking again and spraying Miracle Grow. Not much difference. You need moisture, decent soil, fertilizer and sunlight. Some people do like to amend the soil with peat or fertilizer or top soil. If you have decent soil, that's not always necessary.
Scott's and other manufacturers make a patch mix with seeds, fertilizer, and cover protection all in one large bag. I've tried this. It works, but it is very expensive. I'd recommend it for patching small areas, but if you are going to use it for a large lawn, it's going to cost you a fortune, and probably not do much better than if you put a little sweat equity into raking and spreading and raking and watering and fertilizing yourself.
Good luck.
