How should I use this laser diode from eBay?
If you mean to use them continuously you will want to heatsink them. Otherwise yes, you can just apply 3V. All the circuitry needed is in the attached driver.

Be aware that many such cheap laser modules are underspec, so it might not actually output 50mW of green light.

Another thing to keep in mind is that this isn't actually a green laser diode. It is a DPSS module, meaning it is an infrared laser diode pumping a crystal pair which is what creates the green laser light. This makes them quite unstable, output is highly dependent on temperature, and the module can be damaged by shock that disalign or shatter the crystals.