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.
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.