Alright what your gonna wanna do is rent a thatcher and run the across your turf 2 or 3 times and rake up the mess or suck it up with your mower, then depending on how well your current soil drains your gonna wanna get a load os either a good 60/40 mix or just straight sand, assuming the trees are the property line you could probably get away with one yard. Throw this down even and rake it smooth. Get more than enough seed, I don't know what grows best in your area I use a perenial/rye blend. Put down the seed heavy. Now get a good starter fertilizer should say 16-16-16 on the bag. Keep this good and moist until your seeed has germinated and is about 4" tall before you mow the first time. Fertilize minimum twice a year spring and fall. The fall feeding is very important and will do a lot to prevent this from happening again.