cardboard or several sheets of newspaper should be fine. It also depends on what type of grass you have. If you have Bermuda grass or nutsedge, the smother might not work. For regular sodgrass like rye of fescue it should be fine, though. Personally, I broke up the subsoil under the bed because it was pretty hard, and I wanted the roots to be able to grow into it. If your soil doesn't start out hard that shouldn't be necessary, though.

Iremoved the sod, tilled about six inches and then built raised beds 10 inches high over that. I have had very few weeds in 3 years and am able to have really good dirt! Good luck.