We have one and use it a lot when we are at anchor. It works wonders in eliminating transom slap. Bill is correct that in a marina we have not had to use our Slap Silencer, but whenever we are either anchored or tied to a mooring, we use it a lot.
To answer the original question, the SS comes in a cylindrical bag that is easy to store. The base is about 6 or 8 inches in diameter and the length is about 3 or 3 1/2 feet long. We store ours in the wet locker.
The SS has a mesh on one side that does trap some debris. Usually I hose out the mesh side and hose off the SS first thing when we get back to the dock and hang it out to dry while cleaning the rest of the boat. In the sun, it dries fast enough. If not, I hang it up in a head and stow it away next trip to the boat.
If you are having issues with transom slap, I highly recommend this item. It works like a charm.