I cook a turkey on the Weber every Thanksgiving and several more during the rest of the year. I use to cook them in a roasting pan on the cooking grate indirect. The last few years I have spun them on the Weber using a rotisserie (thanks to urging and prodding by
@Travis ). The weather in California around Thanksgiving is usually in the 50's. I start out 25 lit briquettes in each charcoal basket. I add 9 unlit briquettes per side every hour. A 14lb bird will usually take about 2 hours on a Weber. Figure about 11 minutes per pound in computing cook time. Make sure your bird is totally thawed and remove it from the refrigerator 2 hours prior to cooking.
Also, arrange your charcoal baskets more to one end.
When you place your turkey on the grill, make sure the legs and thighs are closer to the charcoal baskets. This allows the breast to be slightly further from the heat source and helps keep it from overcooking and drying out. If you want some smoke flavor, add some apple wood chips or small chunks at the very beginning. Using to much wood can turn the skin very dark. I like the skin to look like this
as opposed to this. I went overboard on the apple wood chunks on this one
As addicted-to-smoke suggested, do a trial run prior to Thanksgiving. Work out the bugs before the big day, plus you will have a wonderful dinner and turkey for sandwiches.