Experts and BHG readers answer.
Removing lawn and replacing with stones
An application of Roundup should do the trick. Then, put landscape fabric down before you spread the mulch or stone. Should work fine that way.
You could dig the grass out by hand, then put down the fabric, and you'd probably be fine that way too. But this isn't very practical unless it's a very small area -- sod can be a lot of work to dig out! Spraying is definitely the easier way to do it.