There is more than one right hand
rule. To the best of my knowledge, there are actually several. The first one students encounter is the one that represents the
Lorentz force law and is described very well above.
The second most common right hand rule is useful for determining the direction in which magnetic field lines propagate when a current is passed through a wire. To utilize this rule, loosely make a fist but stick your thumb completely out, like you're giving a "thumbs up" sign. Your thumb will represent the direction of the current's flow. Your fingers will dictate how the magnetic field lines curl around the wire, as if the field lines were originating at your knuckle and proceeding around towards your fingertips.