I have a hand to model, but I want to make the opposite hand from it first. I tried mirror modifier, but it just gave me fingers growing out of both ends.
Try changing the mirror axis in the modifier tab.
The Mirror modifier mirrors across the object’s Origin (the yellow dot), unless you specify another point in the “Mirror Object” field.
So to avoid self-intersection, you either have to move the geometry aside in Edit Mode - or move the origin in Object Mode with ctrl+alt+shift+C.
You can also mirror “manually” in Edit Mode with ctrl+m, then X/Y/Z. The center point is based on your current pivot mode.