The Right Hand Rules
There are a few rules that we should always remember. Keep in mind, however, that the currents mentioned are always conventional current. If you'd like to use the current flow of electrons, everything remains the same except you use your left hand.
Now, the most commonly used hand rule is shown and labeled below. As can be seen, the direction of thumb is the conventional current, the direction of the other fingers is the magnetic field, from north to south, and direction of the palm is the direction of the force exerted by that system.
Another right hand rule, illustrated below, simply shows how a current-carrying wire generates a magnetic field. If you point your thumb in the direction of the current, as shown, and let your fingers assume a curved position, the magnetic field circling around those wires flows in the direction in which your four fingers point.
One of the variations of the right hand rule is Fleming's Left Hand Rule, commonly used on current carrying wires, shown below:
Just to confuse things a little, you can also use another right hand rule to illustrate the same principles that Fleming described with his left-hand rule. Point the thumb of the right hand in the direction of the current and the rest of the fingers in the direction of the magnetic field, which extends from the north pole of a magnet to its south pole. The direction that the palm is facing when the hand is in this position is the direction of the force exerted on current (charged particles), called the Lorentz force, but that's for another time.