Using a spray bottle with Apple Cider Vinegar, keep the butt/shoulder moist for 4 to 5 hours. I'll spray it about every 30 or 45 minutes.
Next, I apply the dry rub. Mine will vary sometimes but I usually use a generous coat of coarse (or fine) black pepper and then kosher (or sea)salt.
Next, I'll wrap the butt/shoulder in alum foil and place it in the refrigerator overnight.
Take the butt/shoulder out of the refrigerator and let it stand at room temp for about 4 hours. I like it to be room temp before putting it on the cooker.
I'll get the cooker to 215-225 degrees and then put the meat on the grill with the fat side up. I place a meat thermometer in the center of the meat, away from the bone, and let it cook. I usually allow 90-120 minutes per pound for cooking time. And, I'll cook it until the thermometer reads 175-180 degrees, internal meat temp.
After it's through cooking, I'll form a tent with alum foil and cover until it cools enough to tear the meat apart for sandwiches. This usually takes about 30 minutes or so.
Side Note: If you prefer, you can turn the butt/shoulder after 3 hours and put the fat side dwon (your choice). Cook it fat side down for 3 hours. And for the remaining hours of cooking, you can wrap the entire butt/shoulder in alum foil and cook to desired temp. I seldom turn mine as the rub has created a "shell" so to speak and it'll crack and fall away.