There are all sorts of ways to display a ship model. Since I'm not sure what sort of ship is your favorite I can only make some general comments, but here goes.
One popular and dignified way to show off any kind of ship is with a pair of pedestals. The usual material is brass, but mighty nice pedestals can be made from wood. If you don't want to make them yourself, various sizes are sold by such firms as ModelExpo and Bluejacket. Most of these have grooves in their tops, to accommodate the keel of a sailing ship. You can saw and file the top flat if your ship has a flat bottom.
Another common source of pedestals is the lamp department of the local homeowner's store. A display of lamp repair parts will usually include some finials that can be reworked into pedestals. There are two problems here, though: the range of heights and diameters is severely limited, and so many other folks have done the same thing that knowledgeable observors will immediately recognize the lamp finials for what they are.
The spacing and height of the pedestals are crucial to the finished model's aesthetics. I don't know of any hard-and-fast rules here; I do know that a model sitting on pedestals that are too high, or spaced to far apart, looks pretty awful. Maybe the best approach is to work out the problem on paper first. Get a drawing of the completed ship (e.g., the drawing on the instruction sheet) and go to work with a pencil. Draw in a hypothetical pair of pedestals (maybe three if it's a big ship) and adjust the spacing and height till they look right to your eye (which, after all, is the eye that matters most).
Another nice way to mount a full-hull model is on "keel blocks." A row of closely-spaced blocks made from some nice hardwood (say, walnut or cherry) looks vaguely like the blocks used to support a ship in drydock. The ones at the bow and stern are narrower than the ones amidships. Done carefully, this can be a really nice display system that heightens the aesthetics of the hull.
It's vital to plan the display method early in the process of building the model. Some sort of mechanism for attaching the hull to the base needs to be built into the hull. It can take the form of a thick block of wood, or a couple of nuts (the threads matching those of the mounting screws). But if you don't think about the mounting method in advance, the model will never be stable.
Whatever mounting method you use, the model obviously needs to be fastened to some sort of baseboard. If you have access to some basic woodworking tools you can of course make it yourself. If not, the aforementioned ship model companies sell pre-cut baseboards with routed edges in a variety of sizes. If circumstances permit, it's a good idea for the baseboard to be considerably larger in width and length than the model. (Some people mount sailing ship models with their yards and bowsprits overhanging the baseboards. That's a recipe for disaster.)
The final touch is a nameplate - traditionally of brass, but nowadays you can crank out a nice one on your computer. Woodworking companies (try <www.leevalley.com> or <www.rockler.com>) offer brass, steel, and pewter "card holders" that make nice frames for computer-generated name plates.
The exhibit case is another topic.
Hope this helps a little.