Chela - eden is right, as far as he went. I would add that you want to clean up ALL loose dirt & debris first. To the extent you can, get the crud from between the plates and the floor, etc. with a putty knife or similar. Then, scrub down all exposed studs, plates, joists, floorboards, etc. with detergent and water, using a scrub brush to get into the surface porosity of the wood. Let it dry thoroughly. If you have access to a moisture meter, we'd like to see an indicated moisture level of 14-16%. If not, a good rule of thumb is to let it dry at least a week in ambient conditions. At that point, apply household bleach solution, mixed 10% by volume with water. You can use a pump up garden sprayer for this. Get every surface wet with the solution. Let it dry, same as above. Don't forget to protect yourself from the bleach (Tyvek, gloves, and an N-95 from the office). If you want to gild the lilly, apply a top coat of antifungal coating.
There is no mold "certification" - I've been advising to take some digital pics while the work is in progress to document - the bleached framing looks great when you've finished.