AwkwardSaw's definition of the right-hand rule (interchangeably known as the right-hand grip rule or right-hand screw rule in my physics class) can also be used to do the opposite: given a solenoid, determine where the north pole of a magnetic field is when current is run through the solenoid. Simply hold your hand out flat, curl your fingers around in the direction that the current is flowing, and extend your thumb. The north pole is at the end at which your thumb points.
The right-hand slap rule is another variant of the vector multiplication rule. Using the Lorentz force example, the thumb indicates direction of current (first vector), other extended fingers indicate direction of magnetic field (second vector), and the palm represents the direction of said Lorentz force (resultant vector). Why "slap"? Move your hand in the direction of the resultant vector, it makes a slapping motion.
Another method is, of course, the left-hand rule - exactly the same as the right-hand slap rule, except the first and second vectors are swapped. Oh, yeah, and while I'm here, I should mention this XKCD comic: it shows three more alternative rules for multiplication of vectors.