Teresa, this may or may not be the best approach for you, but here's what I do and it works great...
In the fall or winter prior to the spring you want to plant, just take a shovel and turn over all the grass in the area that will be your garden. The turned over grass will deteriorate over the 6 month period before planting and it makes fantastic compost. You'll have an organically fertilized garden next spring that grows great!
You will have a few grass shoots come up in the spring, just take a shovel or spade and either turn them over again, or remove.
Good luck!