Replacing a broken shower drain is sometimes tricky because many have difficulty removing the old drain. It is not only screwed in, but a layer of putty also helps hold it in place. However, once you remove the old drain, doing the actual replacement is relatively easy.
Purchase a replacement drain. Insert both "needles" of a pair of needle-nose pliers into holes in the old drain cover. Be sure the two needles go in different holes. Insert the head of a large screwdriver between the needles.
Push the handle of the screwdriver in a counterclockwise motion, effectively using it as a lever against the pliers. When the pliers turn, so will the drain. You may need to use some force at first to break the putty's seal, but then it will unscrew easily.
Remove the old drain cover. Squeeze a thin layer of piping caulk around one ring of the screwing threads on the base of replacement drain. Insert the replacement drain cover.
Screw it in tightly. Do it the same way you removed the old drain, but turn everything clockwise. Let it set for at least an hour before using.