Sheet mulching is a technique anyone can use to kill off most of a lawn without herbicides. It's almost as easy as herbicide and, instead of introducing poison into your home's ecosystem, the dead grass actually will supply nutrients to the crop you eventually plant where your lawn used to live.
Sheet-mulching is easy and effective. The main drawback is that most of us want our gardens planted and producing yesterday. Too bad that attitude is not very gardener-like. A garden takes time and love and really doesn't come into being until the fifth year or so of planting. And no matter how good of a gardener you are, it will take several years for you to acclimate yourself to any new garden site. That's not a bad thing, but it rubs most folks in our society the wrong way - which is why we are so apt to use poisons and employ gas-powered tools to make it the way we imagine it should be. Both of those methods kill the organisms in the soil and require a gardener to do a lot more work and spend a lot more money than was necessary in the first place.
Relax! It will take time - allow your garden to flow from season to season. Stop trying to control it as much and begin to see yourself as one who helps the process along. Plants want to live and to produce. Try to stay out of their way and enjoy the process.
It's a lot better for your peace of mind and your heart.