There's really no mystery to serving wine as most of us can manage to get the wine out of the bottle and into our glass without too much trouble, but here are a couple of things that may help the wine show its best:
Temperature: In general, white wines should be served chilled and red wine at room temperature. For whites, a couple of hours in the fridge will do just fine. If you're pushed for time, then put the bottle in an ice bucket filled half with ice and half with cold water. This will bring the wine down to the desired temperature in about twenty minutes. For most reds, room temperature is ideal, unless the room is a balmy 80°F, of course.
We've all had warm red wine served to us in restaurants and, frankly, it does the wine no favors. Light, fruity reds, like Beaujolais, are best served a little cool, especially on a warm summer day. Champagne, dessert wine, most sherry and rosé should be treated as white. Red port should be served at room temperature but tawny port can be chilled.
Decanting: This is the process of pouring off any sediment that has been deposited in the bottle over time to create 'clean wine'. It is frequently done with vintage port or older red wines that have spent many years in a bottle.
The vast majority of wines do not need to be decanted at all, but if you do need to do it, simply pour the wine slowly into a glass decanter or jug keeping an eye on the neck of the bottle. When you see sediment in the neck, it's time to stop. Decanting can also help the wine "breathe".
Breathing: If a wine has spent many years locked up in a bottle, away from the air, it will benefit from a little breathing time. This can take place in the glass or in a decanter and twenty to thirty minutes should suffice.
Even young wines can benefit from a little breathing time as it allows the wine to open up and really show what it's made of. You can test this by tasting a wine immediately after opening it and then see how your second glass tastes some twenty minutes later. There's often quite a difference. That's also why, if you're opening several reds, open them all at once. You give your next bottle a chance to breathe, while you are enjoying the current one. On the other hand, whites generally don't need to be opened ahead of time, as the goal is usually to retain their freshness.
Glassware: The best glasses for appreciating wine are made of plain, thin, clear glass. Heavy, cut glass makes it difficult to see the wine properly. The glass should have a wide bowl tapering to a narrow opening; a tulip shape, in other words. This allows room for the wine to be swirled in the glass while concentrating the aromas at the rim.
Champagne should be served in tall flutes or tall, thin tulip-shaped glasses. Today there are many specialty glasses designed to be used with different grape varieties. While these may, indeed, enhance the attributes of the different wines, they really aren't necessary. A good, all purpose glass like Riedel's "Ouverture" series red and white wine glass, is a simple, elegant solution for about $7/glass.
Fill level: The glass should never be filled more than about half full. This allows room for swirling the wine around in the glass to release its aromas without splashing it all over the table. A good way to achieve this is to leave the glass on the table, hold the stem at the base and make small, quick circles with the base. Try it!
Always taste the wine yourself before serving it to guests in case it's faulty.
If you don't finish the bottle, most wines will keep quite happily for a couple of days with the cork stuck back in the bottle, keeping the air out. You can even buy vacuum pumps in wine shops to remove the air altogether, which will buy you another day or two.
Whites are better off in the fridge and reds left out at room temperature. It's impossible to say exactly how long a wine will keep once open because each wine is different, but in general the higher quality the wine, the longer it will keep.