Courtesy of Bingo B. Boise, ID
Depending upon what kind of grass you have, grass can regrow itself from the live roots. Some grass varieties are more invasive than others. So just rototilling it under can actually create more grass plants in your lawn than before. Converting an existing lawn is hard work. It can be expensive too. I've done all of these at one point or another.
1. Rent a sod cutter and cut out the grass. Rototill after you remove the sod. Use the pieces of sod to create berms or earthen raised areas. On one garden I put an ad on craigslist and people came by and picked up the sod. On another I created a circular bench out of the sod pieces using them like bricks. The plan this year (now that all the grass is basically dead on those sod pieces) is to encase it in real bricks with a flagstone top to create a bench-like wishing well feature.
2. Hand dig out the sod. The easiest (actually it is all hard) way is with a pick using the flat side to cut up under the sod. (See #1 with what to do with the sod.) Or, you can use a flat edge shovel and cut out square pieces. Make sure you get down about 3-4" (look to see how deep the thickest grass roots go.
3. Double dig and put the grass/sod/root piece really really deep. I've tried this way and still have a grass problem.
4. The "lasagna method". Do a search in the SPIN Online Support group discussions for details or google it.
5. Solarize using clear plastic(not black). This will take about 90 days of your hottest weather and usually an entire season. You want the grass to have a nice warm environment to grow, like a greenhouse. Then when it gets really hot under there with no water they all die. It even does a good job on weed seeds too. This may take longer than you want.
6. Chemical Herbicide---uck. Not recommended.
7. Make raised beds on top of your sod with a really thick layer of cardboard or newspaper between the sod layer and your soil. You have to bring in all new soil for this one and it can be costly.