It's as complicated as you want to make it, but a few basic rules to matching food and wine will go a long way…
Match weight with weight
Food and wine matching is all about balance, and much of the terror can be removed by pairing up on the basis of weight rather than taste to start with. Thus, light food with light wine and full-on food with full-bodied wine. It's not a bad way to split up your wine list, in fact.
Within the "weight categories", there are certain flavours that will go better than others, but the problems of food dominating the wine or vice versa should be eliminated.
Red isn't just for meat
The old rules of "white for fish, red for meat" no longer stand up. Turkey, for instance, is a white meat but most people drink a light red (typically Pinot Noir) with it. The same goes for "meaty" fish like tuna or even monkfish, which also work well with mid-weight reds.
Classics still work
Why do people serve oysters with Muscadet, lamb with Rioja and beef with Bordeaux? Because they work, that's why! A great food and wine match doesn't have to be inspirational - just effective.
Think regional
I'm not suggesting you have to have Chianti with your pasta, but if in doubt, it can be handy to think what the locals would drink with the dish. Thus, for a creamy pork dish I'd head for Alsace (where they eat a lot of this kind of food), probably with a good dry Riesling. Likewise a big homely peasant French stew needs a big, homely, rustic wine - say, from the South of France.
Handle with care!
There are some food profiles that are incredibly hard to match with wine. Vinegar is one (so anything pickled won't work), anchovies are another (so watch those pizza toppings!), while salty blue cheeses really need something sweet or chunky and fortified.
Hot spicy foods are tricky, too, since tannin in red wine exaggerates the spice and can make for a real burn. With hot dishes I'd go either for a good fleshy white (preferably with a bit of mouthwatering acidity) or, if it has to be red, I'd suggest the following: New World, rather than Old (we want that soft, sweet fruit); not too much (hot) alcohol; lushness rather than complexity.
Since the dominant flavour in curries and the like is the sauce itself rather than the meat, it's perfectly possible to have, say, a bottle of Pinot Gris or Gewürztraminer, with a lamb curry.
TOP MATCHES
Steak with Cabernet Sauvignon; game with Pinot Noir; Sauvignon Blanc with goats' cheese; white Burgundy with chicken; Gewürztraminer with Chinese food; New World Chardonnay with Asian fusion food; Lamb with Rioja; seafood with Muscadet; Chianti with veal; Sauternes with foie gras; oloroso sherry/port with blue cheese; Aussie Shiraz with venison.