The one thing that food photography, especially for the web, is not about is a lot of expensive equipment. The gear you have right now is entirely adequate, at least in terms of camera and lens. (That said, you may want to buy a 35mm or 50mm lens with a maximum aperture of at least f/1.8 at some point in the future, not because they're "better lenses", but because they will let you really restrict how much of the dish is in focus—and they're relatively cheap as these things go.) For a lot of types of photography, a kit 18-55mm lens would be inadequate, but with food photography you're almost always working in very tight to the subject, so you don't pay a huge penalty for the smaller maximum aperture. And if you're shooting primarily for the web, your final images are going to be small enough that the slight softness and imperfections of the kit lens are going to be mostly eliminated when the image is resized.
Food photography, though, can be a fairly involved process. What you're doing is normally the job of two professionals: the photographer and the food stylist. The stylist's job is to create the Platonic ideal of the dish and its environment; the photographer's job is to capture that Platonic ideal in pixels (or on film).
Food styling often means cheating a bit. That cheating can range from building a dish on a scaffold that would never be used in an actual plating (like filling the bottom of a soup bowl with glass marbles so that the chunky bits of the soup are forced to break the surface) to misting fresh ingredients to make them look fresh, to oiling cooked elements to make them look juicy. (Believe it or not, WD40 is sort of the industry standard, although you could probably get the same sort of effect using a plant mister or a pastry brush and a light safflower or canola oil without the petroleum smell/taste.) It's not so much a matter of outright lying—you're trying to compensate for the fact that there is only one of the five senses in play in a picture. You may need to undercook and over-char some foods to make them look "real" and appetizing; the food as it's actually served would look overcooked and greyish in a picture. You probably don't want to get too extreme with this, although it can go pretty far (some of the most mouth-watering food pictures ever taken were of things that would not only taste horrible, but would be unsafe for consumption). The food is the bride on its wedding day; the fact that it's never actually looked that way before and probably never will again doesn't matter.
The photography part is mostly about lighting (composition is largely folded into styling). It's not just about getting the exposure right and eliminating unwanted shadows, it's about getting the highlights where you want them. A single, simple reflector (like the white board you mentioned) is good for the gross adjustment of contrast, but you'll usually need to add little pockets of light and shadow here and there. White, black and silver reflectors see a lot of use in food photography—little bits of card, with those triangular fold-out picture stands you can get in most craft stores glued to the back, come in very handy. You can keep them just out of the frame, or hide them behind things in the picture. They're cheap and easy to make, and you really can't have enough of them or have enough different sizes.
The object of the game is to have all of the marvelous colors of the food come through in the picture, and to make everything (with the possible exception of mahtso—even cakes and breads need a little life) look something other than dry. Dry is a killer.
Lighting is easiest if you start with something above and behind the food. That can be window light (through what are variously called "sheers" or "net curtains"), a softbox (if you get commercially serious) or bounced light from a lamp or a flash. That will tend to lend an overall sheen to the entire dish, which is often desirable. It's not a hard-and-fast rule (there are very, very few of those in any genre of photography), but it's a good, safe place to start.
Above all, look at what other people are doing. Look at magazines like Fine Cooking and Fine Dining, along with foodie web sites, and try to see where the lights have to be coming from in order to give the highlights and shadows you are seeing. Pay attention to how the pictures are composed—that tends to follow trends, and being too far away from the current expectations can have a negative impact on how your own photos are received, no matter how technically or artistically good they may be.