The left hand is held with the thumb, index finger and middle finger mutually at right angles. It can be recalled by remembering that "motors drive on the left, in Britain anyway."
The First finger represents the direction of the Field.
The Second finger represents the direction of the Current (in the classical direction, from positive to negative).
The Thumb represents the direction of the Thrust or resultant Motion.
There also exists Fleming's right hand rule (for generators). The appropriately-handed rule can be recalled by remembering that the letter "g" is in "right" and "generator".
De Graaf's translation of Fleming's left-hand rule - which also uses thrust, field and current - and the right-hand rule, is the FBI rule. The FBI rule changes Thrust into F (Lorentz force), B (direction of the magnetic field) and I (current). The FBI rule is easily remembered by US citizens because of the commonly known abbreviation for the Federal Bureau of Investigation.
Right-handed variant
A right-handed variant of this rule is as follows: If the current through a wire is in the direction of the thumb of the right hand, and the direction of an external magnetic field on the wire is represented by the fingers, then the force experienced by the wire will be in the direction the palm of the right hand is facing.