The knee joints shown below have gussets to allow a good connection between upper and lower legs. This same type of gusset could be used for elbows, ankles and wrists, but the joint only allows uni-directional movement. For wrists, this would not provide a realistic range of movement. For a doll, that's fine, but if it's realism you're after, there are other options. Good descriptions of many types of joints can be found in Anatomy of a Doll and Designing the Doll, (see My Reference Books for descriptions).
As diagrammed below, a button joint is fairly easy to make. Align the torso and arms or legs and run a length of waxed linen (purchase through a book binding supply store) through all body parts and two buttons using a long doll needle. Waxed linen is necessary to make a tough, long lasting joint and prevents having to run a thread back and forth through the doll, an exercise in frustration. The linen cord is tied in a square knot and presto, you're done. The benefit of using waxed linen is that the wax (and there's a lot of it) holds the knot. I know it seems like the knot will wear our or come undone, but trust me, neither will happen and that joint will last a long time.
|sketch of thread path, linen and needle|
|A long doll needle is very important|
The little cat is a basic toy. The next guy, a mule deer, is a figure in progress. He's not finished, so it's easy to see his joints before final embellishments are added. He has button joints in the shoulders, but notice that they are not easily visible. I cover the buttons with a circle of cloth, giving the buttons a little camouflage without altering the function of the joint. If a joint will be covered with clothing, I usually don't cover the buttons.
|Can you see the shoulder buttons?|
|The buttons have been covered with matching cloth|
The knee joints shown below are different from those in the cat. Because this figure is meant to be displayed as an art object, I made the knees with beads instead of buttons. The joint is less bulky but still allows realistic movement.
|black beads form this knee joint|