To keep a wine as fresh as possible after opening, you must battle the issue of oxygen and oxidation. There are several things that have been suggested for attempting to reign in the issue of oxidation. First, you want to make sure you store you wine with as little surface area of the wine exposed to oxygen. This means, at a minimum, storing the bottle standing up right as opposed to lying on its side.
You may also consider using the rubber corks that you can then pump the air out of the bottle to further reduce the amount of oxygen remaining in the bottle to affect the wine.
Another technique involves rebottling the wine into a smaller container that would therefore have less air in it. You can purchase these from some wine shops or you could consider saving used half-bottles from previous wines. The fuller the container the less air you have to worry about in the bottle.
There are also systems you can purchase that will pump a gas such as nitrogen into the bottle forcing the lighter oxygen out of the container. Some critics have claimed, however, that the nitrogen affect the wines in both softening the tannins and aromas.