It had always been my intention to make a three-strand nylon snubber bridle, but I never got to it. My current snubber is made of 3/4" three-strand, I think. I spliced it to a galvanized chain hook, and whipped the other end. It's about 15 or 20'. I think I often don't have enough snubber deployed, but it seems to do the job, in that we don't ever feel a "snatch," even in rough conditions.
You have to make sure you have enough slack in the chain between the boat and snubber hook. Let the chain droop in a big loop, into the water.
A chain stopper is a piece of hardware that is very strong, and is attached to the deck in a very secure fashion, similarly to a cleat. It will potentially take the entire mooring load. There are several variants, including ones that are like ratchets, i.e., will allow chain to come aboard, and will catch it going out. I guess there's a way to keep it released when letting chain out, but I am not familiar with them.
After we've rigged the snubber, we wrap the chain around our mooring cleat; it seems to "catch," or jam on this. Sometimes we'll secure it with a small diameter line, a "nip."
Here's a good example, and a good article on this:
http://commutercruiser.com/7-tips-for-using-a-snubber/
Here's a couple of chain stoppers:
