Your first response to discovering mold shouldn't be to demand that the landlord call in the folks with the white suits and ventilators. Most mold is relatively harmless and easily dealt with. Usually, a weak bleach solution (one cup of bleach per gallon of water) will remove mold from nonporous materials.
People with respiratory problems, fragile health, or compromised immune systems should not participate in cleanup activities. If you have health concerns, ask for cleanup assistance. You may want to gently remind your landlord that it's a lot cheaper than responding to a lawsuit.
You should follow these commonsense steps to clean up mold if the job is small. Use gloves and avoid exposing eyes and lungs to airborne mold dust (if you disturb mold and cause it to enter the air, use masks). Allow for frequent work breaks in areas with plenty of fresh air.
For more information on how to clean up mold, check the following resources:
If you discover mold on the property, should you test it to determine the nature of the mold and its harmfulness? Most of the time, no. You and the landlord are much better off directing your efforts to speedy cleanup and replacement of damaged areas. Knowing the type of mold present and whether it produces toxins will not, in most cases, affect the appropriate method of cleanup.
Properly testing for mold is also extremely costly. Unlike detecting lead paint by using a swab kit, you cannot perform a reliable mold test yourself. (Over-the-counter kits, which cost around $30, provide questionable results.) A professional's basic investigation for a single-family home can cost $1,000 or more. And to further complicate matters, there are relatively few competent professionals in this new field and no state or federal certification programs for mold busters.
This said, it will be necessary to call in the testers if you contemplate suing the landlord for a mold-related health problem.