As Mitch says, plugging is the way to go... I wanted to add, that be sure you cut straight down into the ground, not at an angle... and try to lift all of the plug up in one piece... the average plug will be about 4-6 inches deep... the extent of the root system. Keeping the root system intact in the plug ensures that the grass won't die off. Try to avoid the plugging method when the ground is dry, as the grass will stand a good chance of dying off and, worse yet, the plug getting pulled out of the ground by a lawn mower.
I generally cut a good sized plug, about 8-10" in diameter.... this aids in quick and easy target retrieval, and leaving as much grass/roots intact as possible. If you hunt on a well manicured lawn, it is best to stick with a smaller plug.. about 4-6 inches in diameter and leave it hinged on one side. When you put the plug back in, make sure you tuck the edges down good and fan the grass over and around the plug quickly with your hand to blend the grass together back into the original lie. Hope this helps, HH, Mike.