Step 1: right click avy > edit pose > a list of currently playing animations displays and you can choose one. Or right click avy > new pose
Step 2a: big edit style arrows sprout from the current joint (last edited, or hips by default). You can interact with it in all the standard ways users already know about with the build window. Move? Drag an arrow. Rotate? Drag a ring or the grey ball.
Step 2b: The edit window opens to the animation tab, or perhaps a whole new GUI. As a first approximation, imagine grabbing all the stuff from qavimator, squishing it into one or two 'floaters' windows inside the client.
The GUI I imagine for IK, perhaps a tab on the animation editor?
To take advantage of the 'absolute time' feature, you need to edit multiple animations at one time to make them interact well. Each animation could sprout a new line in the time line window. Would need some indicator which is the current animation and way to switch so the numbers boxes and meta info displays make sense. Time between the many animations is synchronised, so stepping a frame forward, steps all animations forward.
Most importantly, if you are granted permission, you should be able to right click on another avy, and choose edit pose.
Now, I described all this as if BVJ's only applied to avatars. They don't. But the commands and behaviours are the same when editing animations for a door, an avatar, or an attachment (to an attachment to...) to an avatar.
If you edit your pose, and the animations of 3 small balls, you could make a juggle animation with balls and hands synchronised. You can make "play catch" animations for two people and a ball. Be a multi-legged creature: add bones, attach prims, animate, enjoy.