I've gone through much of the detail on how to properly grill a backstrap of venison (or elk, antelope, bison, moose etc.) above, but remember that this is done over high heat with the grill top open, and that it takes a good 15 to 20 minutes. Be patient and you will be rewarded.
If you use a barbecue sauce with this recipe, serve the venison with a side salad like potato, macaroni or bean salad, plus maybe some tomatoes and basil, corn on the cob, dinner rolls --- you get the idea. Nothing overly fancy.