You can tell alot about a transformer by looking at it. You don't really mention much other than the number and color of the wires.
It's a safe bet that this is a single phase xfmr from your decription. The green wire is probably connected to the frame and is the gound wire. You might also notice that one of the coil wingings terminates to the same lug as the green wire, or it might be soldered to the frame elsewhere.
The yellow wires are probably the secondary. Wire guage can tell you what the wires can handle from an ampacity standpoint. From there you can start running some tests: short circuit, open circuit. If you're not familiar with these, the internet covers them pretty well, or you can ask here.
Next would be size.... The physical size can tell you alot about what kind of kva you're looking at... is this xfmr the size of a coffee cup or a filing cabinet? The bigger it is, the higher, typically, the kva rating.
Without any markings, it's hard to say, but I'd start with secondary wire size and work my way from there.