> If a home has an active mold problem, it probably has an active water or moisture problem.
Mold can't grow or spread without moisture, so a moisture problem is a necessary prerequisite for a mold problem.
So focusing on fixing any moisture problems is a great place to start. Feeling around walls and baseboards or climbing up into the attic in the hours and days after a big rainstorm is one way to get started without any equipment investment. Air circulation also helps dry things out, so make sure every space has some openings for air exchange.
> or spread
Not explicitly true - dry spores get anywhere dust does.
Whether they become active growth or not is a different question.