Long story short: IR goes through a crystal which turns a part of that to deeper IR which goes through another crystal and BAM! you got green (but only a part of it) The process is called DPSS or DPSSFD.
Not something to be undertaken by anything less than a very persistant and steady handed person, nobody here I know of has tried to build their own DPSS rig, as it is one of the most difficult tasks in the laser hobby.
Very tricky and precise process. All things considered, it'd be cheaper and easier to just buy a premade one.