Remove most of the fat and connective tissue from the raw pork. You'll want to leave some of the far on there for flavor, but most of it should be removed.
Cover the pork butt with olive oil then sprinkle with salt and pepper. Use your hands to cover the pork with the pork rub thoroughly.
Seal the meat with plastic wrap and let the meat rest in the refrigerator for at least 3 hours. Ideally, leave it to marinade overnight.
In the morning, prepare the smoker by adding the wood pellets and either water or apple juice into the base. Heat it up to 225F-250F.
Place the pork, fat side up, on the rack in the smoker. Stick a meat thermometer into the meat and set the base on the smoker. This will help you to know when the pork is cooked through.
Cook for about 90 minutes per pound of pork. The pork should reach an internal temperature of 165F.
Once the pork is cooked through, carefully remove it from the smoker and wrap it with aluminum foil. Then wrap it in a towel and place it in a cooler or similar airtight container. Let the meat rest for another 30-60 minutes. This allows the juices to draw back into the pork and keep it tender.
Carefully remove the pork from its covering and pull the meat from the bones to shred.