First and foremost, ONLY cook with wine you would drink by itself. Never settle for the cheap "cooking wines," they aren't held to the same standards as most other wines. Think of generic cooking wine as the hot dogs of wine, lots of mystery ingredients! Is that really what you want in your dish? I didn't think so!
Don't feel compelled to use the most expensive wine on hand. The high dollar wines have complex, yet subtle notes of flavor, and will only be hidden when combined into food. Go for a tasty midrange wine, or at least stay over ten dollars a bottle.
Understand your pairings. Certain wines work best for certain types of food. Nowadays many markets, liquor stores, wine boutiques and even grocers have handy captions in their wine sections that describe ideal pairings, so you shouldn't find much difficulty, Regardless, a general rule of thumb is as follows: the color of your wine should match the color of your food. For example, chicken, cream sauces, pork, seafood are great pairings with white wines. Beef, veal, marinara sauces, lamb, and hearty vegetables would be ideal with red wines. Of course, it can get much more specific with all of the varying styles of wine that are available, but I'll let your inner Wine-O experiment and find your favorites. My best recommendation to wine newbies is to start with dry wines from each category, don't jump into the complex wines until you've mastered the fundamentals.
How much is too much? If you're worried about drowning your meal in booze, simply start by following your recipe to the tee. No recipe? Just add the wine one splash at a time, until you get the hang of how wine enhances the flavors of your dishes.
Deglazing and reducing. Not only are these a couple of fancy-pants words that make a foodie sound like a culinary genius, but they also serve a practical purpose. Deglazing is the act of, essentially, cleaning a pan with some type of liquid over heat. More specifically, the liquid helps collect all of those tasty pan drippings to use for something awesome, such as a sauce. Once you deglaze, reducing is soon to follow. Reducing a liquid helps evaporate the water and/or alcohol, leaving a more concentrated flavor in the pan. You don't always need to deglaze in order to reduce, but typically you must reduce after deglazing.
Allow the wine to cook in your dish. Don't just add a splash and serve, allow the wine to cook into the food, giving the flavors a chance to mingle, and also let some of the alcohol evaporate. Speaking of alcohol, don't worry about getting a buzz from your food, here's a handy chart from official USDA research on the matter of alcohol percentages that remain in wine/alcohol in a variety of situations:
Boiling liquid, remove from heat
Dishes that have been baked or simmered:
After 15 minutes
After 30 minutes
After 1 hour
After 1.5 hours
After 2 hours
After 2.5 hours
I hope these tips help you expand your culinary knowledge and creativity. Cooking with wine isn't difficult, and it will soon become a very fun and delicious experience. Master these skills and you'll soon become the star of your kitchen!