for the zoas, just slice off a few polyps at the base where they attach using a razor blade. it a clean cut. pat the bottom of the frag dry with a paper towel and super glue it to a small piece of rock (also patted a bit dry with paper towels.) be sure to wear gloves with working with zoas. and wash your hands afterwards. the are known to contain a very harmful toxin.
for the shrooms, decide how many you want to frag. if you only want one frag just tank either a razor blade (or a pair of $0.50 new clean small stainless steel kid scissors work better) and cut it in half. it doesn't have to get the mouth in half, but some say it helps the regrow faster. if you want more than one, cut the top off the base. now cut that top like a pie into however many frags you want. the more you have, the smaller they will be and the longer it will take them to grow. the stump thats still left on the rock will regrow a head and look normal after a little while at which point you can frag it again. to get the shrooms to attach, put them in a container with lots of rock rubble or some sand. cover that with bridal vial. let that sit in your tank for about a week. after they attach to the rock or sand, you can superglue that to other larger rocks in your tank.