If at all possible, lawn repair is better than replacement, especially if most of your lawn is in pretty good shape. Do whatever you can to avoid the need for either a lawn renovation or reestablishment - this is major work!
Repair is fixing only those areas that need it, and giving the entire lawn a good dose of tender loving care with some fertilizer.
The important thing in repairing a lawn is to match the new, with what you already have in place so it's a nice blend. For example, you live in the north and you have a blend of Kentucky bluegrass (very common) and you've got a few dead spots that didn't green-up this past spring - You'll want to plant more Kentucky bluegrass blend. Don't put in tall turf type fescue because you heard it's really great (which it is). They are two different types of grass that shouldn't be mixed.
Now, if the bad areas are small areas less than a foot in diameter, just ignore them - they'll fill by themselves in a month or so. Larger than a foot and then it's time to take some action.
Step One: remove the old dead areas with a shovel. Trim up the sides of the area being removed so they're straight. Fill in the area with new top soil, so the new is level with the old. Now plant your seed. In the south, put in matching sprigs or plugs. For seeds, you can cover with some straw, which is good for areas that might be damaged by a heavy rain. Otherwise, just a little peat moss on top will work nicely.
When planting the seeds, don't bury them in the ground. Use just enough top soil to barely cover the seeds (no more than ¼", with less being preferable). After covering, press down on the dry soil with the back of a hoe, or use your shoe and lightly tamp it down, but don't stomp on it.
Options: There are some products out there that combine a few steps and make it a little easier. Scotts PatchMaster contains just about everything you need: seed at a predetermined rate, fertilizer, and mulch to help keep the seeds properly moist. This works great if you happen to have the same grass type as the package. If not, then don't use it.
Another option is if you can find sod that matches your lawn, you can quickly repair the damaged areas. Follow all of the directions up to the point of planting seed, except for the added top soil. Only add enough topsoil so that with the sod, it matches your existing level. Sod takes about 2 weeks to get established. Keep it watered and don't let it dry out during those first 2 weeks.
Step Two: Apply a fertilizer over the area (follow label directions) that is specifically designated as a "starter fertilizer."
Step Three: Keep the soil moist. For seeds, only the top surface needs to stay moist, but (and this is important, especially if the weather turns hot) it can't be let dry out completely, particularly in the second week after planting. Once the seeds germinate, keep the soil evenly moist and increase the amount of water, but cut back on the number of times you water. In other words, keep the soil moist at a deeper level (moist-not wet!).
Step Four: In a few weeks things will start to move. If possible, don't walk on the repaired areas, and don't mow them until the grass is about 2-3" tall, about 3 weeks after the seeds first germinate. Then you can forget about it and just treat it like the rest of the area.