The first thing you need to know about adding smoke when grilling is that it takes time for foods to absorb smoke flavor. If you are not planning on grilling your food for more than 20 to 30 minutes it probably won't be worth the effort. If on the other hand the dish you are preparing is going to spend more than 30 minutes on the grill with the lid down, then you can consider adding smoke to your grilling. You may notice it. So how to you do it? First you need wood, real hard, dry wood like hickory, oak, mesquite, cherry, etc. Now you need to soak it in water until it is damp. Drain so it isn't dripping, and put it on the grill.
No, don't just throw wood chips or chunks on your gas grill. It doesn't make good smoke that way and it doesn't do any good for your grill. What you need is something to hold the wood in so that it can smolder and produce smoke while not dropping ashes every where. You can do either of two things. You can go out and buy a smoker box for your grill (these can cost as much as $20) or you can wrap the chips loosely in aluminum foil and punch a couple of holes in the top. This lets the smoke out. You can decide which is more economical.
One trick to get presoaked wood chips quickly is to take moistened wood chips or chunks, place them in resealable plastic bags and put them in the freezer. Next time you need wet chips for the grill all you have to do is take them out of the freezer.