This spring a neighbor was laying out his vegetable garden and debated how to remove the grass. At the time I was laying out a shade garden and had been digging up the grass. I recommended that idea, because it seemed like it got most of the grass without getting a lot of the soil. I warned against tilling, remembering how tedious it was picking out all of the pieces of sod from the turned ground. I was probably going to till after all the grass was up, but not until then.
After I did half the bed that way, I was ready to be done and I ended up tilling the rest of the bed instead of digging up the grass. It went a lot faster, but I ran into the problem that I mentioned - all the small pieces of sod that needed to be pulled out. I wasn't too upset, because this is the last time I plan to do this for a while. I'm finding small pieces of grass growing in the shade garden now, but it's not nearly as bad as the first time I did something like this.
The first time I laid out beds, I decided to smother the grass. I had a few months before I needed them, so this looked like a good idea. It was for the most part, but it does take grass longer to die than you would think. Even after a couple of months it wasn't dead. On some parts I think I used black rubber pond liner which got the job done, but didn't look very good. I've had moderate success with newspaper and mulch, but it's time consuming and not completely reliable - I'm having to go back this year and dig out grass that survived that method last year. It seems the best method may be a combination - digging up the grass like I did with half the shade garden, combined with newspaper and mulch afterward. I know - it sounds like a lot of work.