How should I add smoking wood when grilling on charcoal?
Adding wood and allowing it to ignite is the proper procedure. You can do this with the cover on your grill so that it doesn't burn up too fast.  You want the smoke to look bluish, rather than white, for the best flavor.  When you see white smoke, the wood is not hot enough and you will get more acrid, less desirable flavors. You also don't need to see a massive billow of smoke. Catching this at the right time is a matter of adjusting the air flow, and it takes some practice with any grill/smoker set up.  I will also point out that, in most cases, smoke has most of its impact during the first 30 minutes of cooking, so there really is no need to keep it going beyond that.  I will further point out that cooking with hardwood charcoal (rather than briquets) also contributes to the smoke flavor.