I'm not an expert of any kind, but we did have one bad patch of mold, and a few scattered small pathces, in our basement during renovation. We called in an actual mold-specializing cleanup crew for a consultation.
They tested our mold in the lab, and it was stachybotros: the "toxic mold" that has been in the news lately. But by that time our contractor had already ripped out the section that had the mold -- normally the experts would have done that under negative pressure, to contain any spores from kicking up and bothering people who might be sensitized to the mold. Oh well.
These guys were very nice, not looking to drum up business. Mainly, they gave us information on what we should do ourselves.
Anyway: this is the sequence they recommmended.
1. Identify the cause of the mold! Even though basements are always damp, if there's mold in one specific area it may be because there's a gap in your foundation, or in the area where the foundation meets the rest of the house. The latter was true for us: our basement is a walk-out in a split level, the area of the mold is one where the foundation had not been extended far enough -- so the ground was touching wood (bad news). Also, at the end of our renovation we need to deepen our gutters and re-grade the slope, to encourage water to drain away from the house and foundation. Maybe you just have a generally damp basement... but just in case. Leaky pipes are another frequent culprit, if you have any pipes runnning through the ceiling or walls of your basement.
2. Replace replaceable parts that have mold (drywall, etc.)
3. If there's mold on the studs, these should be scrubbed clean: they gave me a specific detergent recommendation, I forget what it was. They also said a bleach solution afterwards would be okay. Same if the mold is directly on the foundation.
4. Ozone: they specifically recommended NOT using ozone generators or ozone air purifiers. I didn't go into detail with them on this, since we hadn't planned to anyway.
5. They DID recommend renting or buying a HEPA vacuum cleaner, and vacuuming the entire affected area to suck up whatever spores are on the surface. Many of these molds have spores that actually don't get airborne. They spread when insects, rodents, whatever, skitter across the mold spores and carry them with them to other areas. So vacuuming with a HEPA vacuum cleaner can be more effective than using a HEPA air filter.
After we did all this, the moldy smell in that spot of the basement, which had been there as long as we had the house (we just didn't know!) was completely gone! And can I tell you how much we love that vacuum cleaner now?
I completely freaked out about the idea of having toxic mold, but they reassured me that as long as the source of the moisture was fixed, and the mold properly cleaned up, it should be okay.
Since we're renovating, and there's useable space in the basement, I'm trying to learn more about what materials to use, which not to use, in order to discourage future mold.
Anyway, the above is not meant as advice or a prescription, but just to give you a sense of what advice was given to us when we called people in.