Laser diodes must be supplied with constant current - constant voltage will either
do nothing or probably blow them up. The current needs to be set close to the nominal
current (too little, no lasing, too much, fried).
The simplest way to do this is to waste power and use a higher voltage (about twice the nominal)
and a series resistor (a power resistor normally, it will dissipate as much as the diode).
The module in question appears (from the picture) to already have a regulator, but we don't
know how much current it needs, but it'll be something around 0.2 to 0.5A I guess (laser
diodes are less efficient than LEDs).
Its pretty clear that this is designed to be part of a torch using lithium batteries, so give it 3.7V
I reckon - if you have a bench supply you can check its regulating the current.
Wear the right laser eye protection for that wavelength, and point it at something matt black
(50mW can burn paper, note).