Same disclaimer as last thread - I am not a doctor - I am an EMT-B with 6+ years experience.
This part of the series is about joint or soft-tissue injuries, assuming minor or no bleeding (see the other thread for that).
In EMT-land, we assess soft tissue injuries with acronym DCAP-BTLS: deformities, contusions (bruises), abrasions (scrapes), penetrations, burns, tenderness, lacerations (tears), and swelling. Use this assessment as your guide for whether to seek medical attention, as well as the level of pain - if you absolutely cannot move the joint, or cannot put any weight on it, it's time to head to a doc. If you know how, take a pulse at the extremity related to the joint (so, if the elbow hurts, at the wrist). If you can't feel a pulse, or the extremity starts changing color, get medical attention immediately. It may mean the injury is interfering with the circulatory system, like a dislocated bone pressing on an artery.
Once it's time to move, whether or not you'll be seeing a doc, it's a good idea to stabilize the joint. Most patients help you out with this instinctively - you'll find the patient holding his joint in what they call a "position of comfort", just because it hurts too damn much to bend it. Have your patient hold the joint in the position of comfort, and then stabilize it so they can let go.
Stabilizing a joint can take some creativity, depending on where it is. Generally, it's done by wrapping the joint with a stretchy bandage. Using a firm, long object like a rolled-up newspaper as a splint can help. If it's an elbow or shoulder, it may help to make a triangle with the two parts of the arm and the splint, or make a sling. Again, make sure you stabilize it into the position that brings the most relief to the patient. Take the patient's pulse at the extremity again to make sure you didn't wrap it too tightly.
Obviously, if there's a deformity or a bone popping through the skin, call an ambulance. Don't try to move the joint or put the bone back. Under NO CIRCUMSTANCES should you try to "pop" a joint back into place. This is not a movie. If you try it in real life, you're an idiot. There are lots of muscles, tendons, cartilage, bones, and ligaments you can permanently screw up this way. Most doctors will do this under general or localized anesthesia - not just to relieve you of the pain, but to relax your muscles to minimize the risk of injuring you further!
Once you get home, there's the classic RICE:
Rest
Ice
Compression
Elevation
Good luck, and hope no one has to use this anytime soon!