Smoke it if you're able. Easy, but it takes a bit of time. You don't need a smoker -- just read
this. (I do, however, recommend investing in a solid wireless thermometer to keep an eye on your temperature.) Also, if you've got a standard Weber grill but no smoker, buy one of
these things now. I've got a Green Egg, but man, I still think I get better results with the Smokenator.
Once you've got the set-up figured out, do this:
1. Dry brine the shoulder -- Coat all surfaces of the should with salt the night before and store it in the fridge covered in plastic wrap. Use no more than 1/2 tsp of salt per pound.
2. Make your rub -- After you stick your salted shoulder in the fridge, make your rub if you don't already have one. You can find dozens of recipes for rub with a quick Google search. The base of these kinds of rubs is usually sugar (often white and brown), paprika, onion powder, garlic, pepper, and some a couple of chili powders (ancho, cayenne, etc.). (Note that since you're brining the meat separately, your rub shouldn't have any salt in it.) Store it in a mason jar or something. Keeps for months.
3. Preheat the grill -- However you're setting up your smoker/grill, get the fire going. You're aiming for 225 degrees, but honestly, shoulders are pretty forgiving. I've had mine go at 250 for much of a smoke with no ill effects, and I've heard of dudes who do them even higher. (As for wood chunks, by the way, just go with hickory. You can branch out to others later like cherry, apple, or pecan, but hickory's a solid place to start.)
4. Dry rub and oil -- As your grill/smoker preheats, coat the shoulder with a thin layer of peanut oil, then rub it down with your rub. Use enough to solidly cover the shoulder, but don't go too nuts. (If you're wondering about the oil, it helps dissolve the spices, many of which are oil soluble.)
5. Put it on the grill/smoker and wait -- Put in on the cooking surface and let it go. As long as you've figured out your set-up, the next while will just involve keeping an eye on the temperature. And drinking bourbon, of course.
6. The stall -- Once the shoulder gets up to 160 degrees or so, its internal temperature may stop increasing for a while. This phenomenon is often called "the stall." To get through the stall more quickly -- and, according to many, to increase the moisture of your meat -- remove the shoulder from the grill/smoker at around 165 degrees (give or take a few), and wrap the thing in a couple of layers of foil with a quarter cup of water or apple juice (or a dry hard cider, which you should by this point be drinking following after the bourbon).
7. Finish it off -- After you've wrapped the thing in foil, you've got a couple of options. You could return the thing to the grill/smoker and cook it till it gets up to around 200 degrees. If you do that, smoke production and temperature control isn't quite as big of a deal as it was earlier on. Or, instead of the grill/smoker, you could put the thing in the oven at at 250 or 300 and finish it in there. (FYI, because of the foil, the shoulder won't have quite as much crunchy "bark" as it would if you had let it cook on through the stall on its own. So some people take it out of the foil and let it go naked on the grill/smoker for another half hour or so to help get some of the bark back. For your first time, though, I wouldn't worry about it.)
8. Fork test -- Is it done? Well, stick a fork in it and twist. If it gives and tears without any fuss, it's done.
9. Rest -- At this point, I usually keep the shoulder wrapped in foil, cover it with towels, and put it in a cooler. It can stay hot for hours that way, which is great if you need to wait to serve it, but the point (I think) is to help moisturize the meat further.
That's about it. Hope it turns out well.