The lens is moved by what is essentially a voice coil. There will be several, oriented perpendicularly, in order to orient the lens in multiple dimensions.
Essentially, they are electromagnets, and a reasonable electrical model is an inductance in series with a resistance:
simulate this circuit – Schematic created using CircuitLab
The current through the inductor creates a magnetic field that attracts or repels from another magnetic field. This force works against a spring or some tension, so as a first approximation, the deflection is proportional to current.
Measure the coils with an ohmmeter to figure out which connections are the corresponding ends of a coil.
The simplest way to drive these is probably with PWM. Limit the voltage and duty cycle to avoid overheating the coils. You probably won't find a datasheet, so determine the limits by experimentation. If you smell something funny, or notice they are hot, try less power :) Most likely, the power you will have to apply to get them to move over their useful range will be well under the power that destroys them.
The frequency response of your actuator (and thus, the sharpness you can get in the corners of your laser pattern) will be improved if you can drive the coils with a current source. This is because the inductance will resist changes in current, so you will get to your target current fastest if you apply a high voltage, then back off the voltage as the current approaches the target.
An even better system also takes into account the mechanical impedances of the masses attached to the actuator. Of course it's getting pretty complicated at this point. Depending on what you are trying to do, a simple open-loop PWM control may be good enough.