Got my new to me 92 XT225 this past Saturday. I took it out for a quick ride and made sure it was running well, then tore it down. Ordered some parts, (new petcock, air and oil filter, clutch lever, fork boots).
One thing that is bothering me is there are two ports on the carburetor with no hoses attached.
One very small black, downward, facing fitting on the left side of the carburetor and a larger, downward facing metal fitting on the right side.
What should these connect to?

The one on the left is a drain tube connected to the float bowl drain, other end doesn't connect to anything. The one on the right is a carb vent tube, the other end doesn't connect to anything.

Yep. Just get most any sort of hose the right diameter and run the end down through the gap between the back of the case and the swingarm.

I'm a little confused. Are you telling me to connect a tube to the fitting on the right side of the carb and also a hose on that tiny black fitting on the left side, and run them both by the swing arm?
Also, is there a factory service manual available for these bikes?

Do a Google search for '1992 XT225 Factory Service Manual.' You'll find there's lots of options for acquiring the manual you're looking for..

That is correct. If you cant find a small enough tube to connect to the float bowl (the one on the left), I wouldn't worry about it, it is not that important. That other one on the right, it might be a good idea to put one on that, to insure no debris entering into the carb from there.