MOLD
You're reading this page because you have mold in your rental. Worse, it's "BLACK MOLD."
First: Don't panic. Just because the mold is black in color doesn't mean it's "that" black mold. Stories on the Internet freak people out with comments about toxic black mold. Does it exist? Yes. Is it common? No. Just because the mold is black, does not automatically mean it is toxic. You are far more likely to be allergic to the mold ( whether it is black, green, yellow, orange, etc.) than to have a toxic reaction, or have mold that is throwing off toxins.
But you have mold. Why? Moisture, pure and simple. If you are seeing and/or smelling mold (musty), there is a source of moisture. Best thing is to find out where the moisture is and eliminate it. (For example, covering your windows with blankets to keep the heating bills down actually creates a moist environment allowing mold to grow.) Not always easy, but necessary.
What can you do now to help clean up the mold? Clean the affected area, and by clean I mean scrub. Mold is a plant, and has roots (hyphae). You must scrub the mold in order to break the roots off from the plant. Clean with detergent, not bleach. The EPA has recommended both at different times. My training says that detergent works better. It can penetrate paint better than bleach (has something to do with chemistry). Then, let the area dry. Then, spray white vinegar on the cleaned area. The pH of vinegar makes it difficult for the mold to grow back quickly. IF the mold does grow back quickly, less than a month, this indicates that the mold is coming from behind the surface (walls, ceilings, etc). It also means that there is a good moisture source that needs to be found and eliminated. Bottom line: don't panic - clean.