Apply fertilizer with a spreader, available at home stores. A walk-behind or motorized spreader is more accurate than a hand-held version. As you move the machine back and forth over the grass, grip the handle like a trigger and it releases pellets when you "shoot." Follow the instructions on the fertilizer package. Apply only the recommended amount. This is not a case of "If a little is good, even more is better" — too much fertilizer can burn your grass.
Provide some extra air for grass roots by aerating your lawn — taking out spikes of soil across your lawn to make holes for planting seed. Aerating is low-cost maintenance and even if it's the only thing you do for your yard, you should see improvement. There are motorized aerators for rent, or manual versions that work like pogo sticks, pushing out two plugs of soil at a time. The pogo-stick versions are good exercise, but beware: the motorized versions can require substantial upper body strength to use.
Purchase grass seed that says "cool season" or "cool weather" on the package, such as most fescues. Scatter it over the lawn with the same spreader you used for the fertilizer, or use a hand-held spreader for less fuss. Try to get the seed evenly distributed so you won't have clumps of grass later.
Drag a rake over the lawn to break up soil clumps and cover the seeds a bit.
Water the lawn with the garden hose, using a nice gentle spray like rain. After that, keep the soil moist but don't overwater it or let it dry out. You may have to mow your lawn a few more times before the cold weather sets in, and you can also fertilize another time in a few weeks to help the grass grow. During the cooler months, you should see a lot of growth as a result of your labors.