Right hand rules

[Pseudo Statistic]

Hey,
We recently started learning about magnetic fields and forces in physics and we took these weird right hand rules...
After much attempt I cannot, for the life of me, figure them out.
Is there any way I can find the direction of the field or a force without using my right hand? Like on paper or mathematically or something? (Choosing "approximate directions" ofcourse)
Thanks for any responses.

[hypermorphism]

The right-hand rule is a mnemonic for the cross product. The algebra of the cross product is already oriented.
However, for quick reference, you should just use your right hand (http://en.wikipedia.org/wiki/Right_hand_rule).

[Doc Al]

Be sure to check out these right hand rule animations (http://physics.syr.edu/courses/video/RightHandRule/index2.html).