Hi Matt,
To frag a Litophyton, you can slice off a whole branch which grows from (and is attached to) the main trunk. The lower branches (in fact, often the lowest branch) are better candidates for fragging, as they are often fatter and more developed than the upper branches.
Use a very sharp knife (as Tommy suggested, I use a sashimi knife; you can also use a stripping knife), and make the cut as close as possible to the main trunk of the original coral. And try to make the cut with just one smooth, swift stroke (to lessen the stress on the coral).
After fragging, place the mother coral back to an area of good flow. There may be slime oozing from the cut, but this should heal soon. Make sure that no other livestock (especially algae) comes into contact with the open cut. And just in case, check if any nosy fish or invert will nip at the open wound.
For the frag itself, you should keep it also in a quiet portion of your tank with moderate flow. You can induce this to stick to a rock (or any substrate of your choice) by several means:
1) just let the frag lie down on a bed of several small rocks, and it will eventually connect to one.
2) loosely tie the frag to a rock, with thread or rubber band.
3) stick the frag to a rock, using a pin or a toothpick.
Either case, in a week or two, the frag should have attached itself to your desired substrate.
IME, this will work well for Litophyton, Nepthea, Capnella, and the tree-like morph of Sinularia. I am not sure (actually I have no experience) in doing this for Stereonepthya and other related tree-like non-photosynthetic corals.
Good luck!
Phil