[sting88]

If I have a drywall butt joint with one side clearly much lower than the other like in the photo, how do I begin?

Should I try to bring the low side level with some joint compound before taping so that the tape goes on flat?

Or tape right away? The tape will end up like a "stair," though with a big edge!

 

[Scuba_Dave]

If the small piece of drywall is much lower remove it & shim it until it is level with the existing drywall

 

[Ron6519]

If you'd rather not shim it out as Dave suggests, you can just tape over the surface disparity. Just apply the compound so the sufaces are level and press in the tape gently. You will need to spend more time compounding this if it's not level, but it can be done.
Spending the time to level it would be my choice.
Ron