It has been done, but it isn't a task for most people. First step is acquiring the basics: An 808nm pump diode >200mW, an Nd:YVO4 rod with the appropriate coatings for 1064nm lasing and interface to the crystal, the KTP crystal with appropriate interface to the laser rod and tuned for 532nm output, and any optics you may choose along the way. You will also want a good TEC to keep the pump diode cool. The alignment is not easy, so you'll need precision mounts for each component as well.
Keep in mind, this is a simplified version of what all would be needed for this to work.
no doubt it would be MUCH easier and cheaper to buy one. As I don't own a greenie, I can tell you from very limited experience seeing those that others own, that in bright sunlight it takes quite a lot of power to be able to see the beam unless the air is very dirty. A friend of mine got one of the DX 50mW models and unless there was some dust we couldn't see the beam outside during the day except when looking along the beam from only a foot away from the beam (not into the beam, along side it)
*much* easier to buy a cheap one. even the beam of a 5mW will be faintly visible outside in the dark, though you may want a 15-30mW-ish one if you want it really visible in the dark. the beam of green lasers even up to about 115mW are always hard to see if there's a lot of light though.
If you want to experiment with it it would be easiest to just buy a low-power greenie and rip it apart. We did some crystal pumping experiments a few weeks ago and it was really neat to see all the different modes that you can create with an 808nm pointer and a crystal set!