Need Help...best way to remove, kill, & keep mold from coming back!?

Ok so I'm trying to spruce up my partially finished basement.It has one room finished with no carpet and one wall with drywall and paint on it, the other walls are concrete. I'm not putting carpet in, rather I'm painting the concrete floor. This space is going to be a play room and possibly a room for my oldest to sleep in. The problem is at one time a window was left open and mold has began to grow on the drywall and on the one bedroom. I'm not sure how long it's been down there as to right now I don't go down there too often but I've kept an eye on it recently and it doesn't seem to be growing anymore and the window was shut so the problem of water is solved.So long story short my question is....I am trying to this very inexpensively so removing the wall and wood and such is not an option besides I'm afraid it would disrupt the mold spores. What is the best way to kill the mold and remove it? Or should I just paint kilz over it and call it good. Even though I've read that all it does is cover the problem. I'm trying to do the safest thing for my family. I plan on using gloves and mask but I'm scarred to disrupt things by scrubbing the mold off. What do I do?