Be sure to soak wood chips in water for 30 - 60 minutes before putting on the grill.
When using gas grills it's best to put presoaked wood chips in a smoker box or wrap them in a piece of aluminum foil with a lot of holes in it. This keeps your grill from filling up with ash and clogging the jets. If you are using a charcoal grill or smoker then you can just put the wood directly on the coals (once they've heated up).
If you haven't used wood before, start small. Use a 1/4 cup of presoaked chips on your grill and see what is does for you. One of the great things about barbecue is the wide variety of experimentation available to the backyard cook. Wood is a great tool so don't be afraid to use it.
You can make a homemade smoker box by using a tin can. Poke some holes in the can, then open the lid not quite all the way and fill with wood chips that have been soaked in water for an hour. Position the can on the coals before grilling. Wait a little bit until the wood starts smoking, and commence with grilling.