If you have a branching coral, all you have to do is cut the base of the branch below the tissue line. The branch is the calcified mineral deposits the coral has excreted as it has grown, and is essentially the discarded skeleton. Just get a good pair of sharp scissors and you should be able to cut the branch right off. And if you nic the tissue, don't freak out. As long as most of the base remains unharmed and your water params are high, it should heal its self in no time. You can also give it a quick dip (Try Tech-D By Kent Marine), if you are worried. Once you cut the branch off, place it where you want it in your tank and base it with marine cement or your choice of adhesive. Simple really. Branching corals like this are the easiest.