I use a can of nitrogen/argon. Two squirts into the bottle, then put the cork back in. The argon is heavier than air and so settles on the top of the wine surface in the bottle. It will keep an opened bottle nearly as good as if it were freshly opened for a week or so. And it's not expensive - a can with about 50 uses is about $10.

In general, what people have said above is correct so I won't repeat it. And do check out the boxed wine - a box of decent wine costs about $20-25, contains the equivalent of 4 bottles, and stays good for up to a couple months after it's opened. I generally keep a box in the fridge for when I want a glass of wine but don't want to deal with the commitment of opening a bottle.

If you're just getting into wine, remember to completely ignore what wine snobs say. Yes, wine has that level of complexity if you're that in to it, but a few hundred million Europeans just drink it and don't make a fuss over it. Explore and taste, then taste more with your favorite foods and see how the flavors change. It's a difficult thing to do, but someone's gotta do it.