The two keys to storing a wine properly are temperature and humidity. That's it. Old stories about vibrations are just that - stories. Scientific studies have been done, and there is no sign at all that vibrations affect a wine. It may stir up the sediment, but nothing more.

Temperature
Temperature is by far the more important of the two factors to watch. The "golden temperature" for wine is 55°F. Wine should normally be stored between 50-60°F, although a range of 45-65°F is considered OK and the most easily maintained by the normal collector. A lower, colder temperature causes the aging process to slow down, preventing the wine from aging properly. A higher, warmer temperature causes premature aging, although not in a "good" way. You cannot just put a bottle of wine in a desert and cause it to age 20 years!

If a wine is kept over 85°F for even a single month, irreparable damage is done to it. What hurts wine the most is temperature fluctuation. Even a steady storage at 65°F is better than storage that every day goes from 45°F - 65°F and back again. One of the effects of this gyration in temperature is that the cork is pulled in and out, and air has a better chance of getting in to the wine. Once that happens, you can kiss your aging goodbye. A good digital gauge makes this much easier to watch.

Note that cold temperature can be just as bad. Don't store a bottle of Champagne in your fridge, waiting for the perfect day to drink it. When that day arrives, the Champagne won't be much to celebrate. You can keep wine in the fridge for a day or two, but if it looks like you'll need longer before you're ready to open it, bring it back down to your cellar.

Humidity
The second factor to watch in your wine storage area is humidity. Humidity fluctuations aren't nearly as bad for wine as temperature. The prime reason to watch humidity is because a high humidity hurts the labels, which hurts the bottle's resale value. A low humidity dries out the cork, even if the bottle is properly stored on its side in order to keep the cork moist. This could let oxygen into the wine - a rare occurrence, but still something to be watched for.

So, in general, a medium-high humidity cellar that stays dark is the best place to store wine. There are many firms that sell either modular components to rack the wine in, or even specialized contractors to custom-build your cellar complete with temperature and humidity controls. 

Every wine has a different ideal length of aging to bring out its best flavors. This depends on the type of wine, the region the wine was made in, the technique used to make it, and the particular year the grapes were harvested in. As a general guideline, whites normally do not age for long, while reds age for 5-10 years. It all comes down to what you yourself enjoy best, but if you're starting out, aging charts help you see when a wine is typically best enjoyed.