First, try adding just a half cup or so of wine to the pot when you've finished searing the meat and sautéing the vegetables. The wine will help to dissolve the caramelized bits stuck to the bottom of the pan and bring them into the dish. Let the wine simmer until it's nearly evaporated to concentrate the flavor before moving on to the next step in your recipe.
Second, you can add a literal splash of wine at the very end of cooking. Because the wine isn't cooked for very long, many of its more delicate bright, acidic, and fruity flavors will be preserved in the dish.
Adding wine at either or both of these times is a really simple way to start playing around with a recipe without going too far into unknown territory. Try it with soups and pasta sauces, especially. Whichever wine you have open is a candidate, from a pinot noir to a shiraz. Also, don't feel limited to only red wines — though their flavors can be more subtle, white wines are great for cooking, too.