Spray the existing "grass" with Roundup or cheaper substitute to kill it around Labor Day. After a few days I recommend you plug the yard and then seed. If you lightly sprinkle the yard a couple of times per day you will have grass coming up very quickly. Most folks also apply fertilizer when they sow the seed.
Once the grass is established I get lazy and use a lawn service to keep the yard properly fertilized and to keep the weeds under control. My yard is beautiful and is weed free!