There are several ways to move it depending on what it's attached to and your willingness to get crazy!
My first try would be to take the rock it's attached to out of the tank and cut the rock just below the spot where the coral is attached. I'd try a dremel first. The new battery powered ones are GREAT! And you'll find lots of uses for it later. If not that, how about a tile wet saw, they are pretty cheap at HD & Lowes (under $100) and will also come in handy later as well. Finally, you could try to use a chisel and hammer. It can work, but it's very imprecise.
You could take something like a credit card or a plastic glass scrapper and try to pry under it's foot. If you have any initial success it usually gets easier as you get more lose. If it's impossible to get a start, don't keep digging as you can damage the foot.
Depending on how big (or small) it is, you could cut it at the base. Leave the cut coral in a container for a few days doing 2 or 3 water changes every day and a new tough foot will develop. Than you can attach it to a new rock. Or you can hold the cut edge of the coral to the new rock with some kind of mesh and the new foot should attach in time but it may take a couple of weeks. You could use fish net material, bridal vale mesh, nylon stocking... whatever. Some people use rubber bands (don't make them too tight or they will cut into the soft coral). I've even used a needle and thread to make a couple of loops through the coral and around the rocks to hold it in place. The part you leave behind on the original rock may very well start to grow a new coral. If you don't want one there, use anything you can to remove as much of the left behind material as possible. Use a blade, an ice pick, an awl, a dental pick... whatever.
