I removed my grass in section over a two year in four sections (spring and fall) to not overwhelm myself with to much work. I outline with a rope the new
garden bed and rolled up all the grass in 1.5 ft. x 4 ft. section which I then posted on
online (kijiji, craiglist...) for free. To my surprised it was gone in a matter of a few hours and people left there contact information which I contacted when I did the next section.
You can also do a lasagna garden but you will need to get your hands on a lot of newspaper and cardboard because you will want to put it on thick to keep the grass from breaking through.
Kris