How to dynamically pose a doll's joints in-game?

I need to know how I can animate a doll in such a way that the user can manipulate each joint individually to create various custom poses. Let's say it starts in a normal T pose. Each joint could have an associated slider bar for each axis, and dragging the bars moves the joint in increments. They could bend the shoulder in so the arm is pointing forward, then bend the elbow in so the forearm crosses the chest. How would I go about creating this kind of dynamic, by joint animation system? I'm confused on both how I could animate it in a way that the joint could move dynamically along the various axis, and on how I could animate each joint individually, leaving the other joints in their relative positions.