Oh boy, been there done that. First and formost, protect yourself. I didn't, working with a bunch of moldy clothes last year, and lost the entire top layers of skin from my hands - and my fingernails are still really messed up. Glove up, and wear a respirator mask: the stuff can make you really, really sick. Seriously.
Mold doesn't like sunlight or extremes of either alkaline or acid. So the best thing to do is clean the stuff off and air it out. If you have really thick, dry mold, take it outside to work on it if at all possible, and scrape it out there with a soft wire brush to get as much off as possible. If you absolutely have to work on it inside, do it over a plastic dropcloth, with the windows open, and use a HEPA vacuum (borrow one if you have to) to get the stuff out of your house - if you use your own non-HEPA vac, all you will do is contaminate your vac and spread it all over your house.
Once you have the worst of it off, get a clean empty spray bottle, and some kind of scrubby, like a dish scrubby, but that won't harm the wood, and lots of clean soft cloths. Fill the bottle with a mild solution of either white vinegar and water or Oxy-clean and water (about a tablespoon of O-C OR about 1/4 cup of vinegar per quart - DON'T use both, either will work.) Use the scrubby if the mold is thick and caked on to brush it off, otherwise, just spray the wood down good, wipe off with clean cloths, and if at all possible let them dry off out in strong sun for several hours. Don't use bleach, it will harm the wood, and it actually feeds the mold. Depending on how finished the wood is, the oxyclean is probably a better choice, it might leave a little white if you don't manage to wipe it all off, but it comes right off with a quick hit with a slightly damp cloth.
Hope this helps. I moved last year out of a totally mold-infested house, and am still decontaminating (and recovering from how sick it made me.) I had to do a lot of research and trial and error to find the best methods, and lost a lot of my belongings before I realized how bad things had gotten. Good luck.