Starting new grass seed can require a little or a lot of labor depending on the route you take. You can grow the seed on the existing lawn and make it a bit easier on yourself, or you can decide to go all out. This will require digging up the lawn and starting over. Some of your decision should be based on how bad your lawn is in its current state. If it is overrun with weeds or has a poor quality soil, then starting over is the better choice.
Kill unwanted grass and weeds if you prefer to start your lawn anew. Apply an herbicide or white vinegar to kill the unwanted vegetation, and then till the lawn under.
Check your soil's pH level with a soil test kit. Grass seed does best at a level between 6.0 and 7.0. Knowing the level will help you proceed and make adjustments.
Add a soil amendment such as lime to your lawn to adjust the pH level if needed. Wear gloves and spread it by hand or use a spreader.
Aerate the lawn with an aerator to break up the soil and old grass if you chose not to till the lawn. Breaking up the soil will help with water drainage and put air back into soil that might have compacted. This will help the seeds grow. There is no need to do this if you tilled up the soil.
Water the lawn to get the soil moist and let any soil amendment soak into the dirt.
Seed the yard with a grass seed that does well in your type of soil and climate. Use a seed that is pin coated if available so that birds won't be as attracted to it. Distribute the seed by hand or with a spreader.
Lay down straw over the seed to protect it from being washed away by rains and hold it in place while it grows.
Water the lawn again to soak the seeds. This will help start the germination process.