Marissa, Here's dh to answer you:
Hi. I am a certified air conditioning contractor in 4 states, so I have some expertise in what you are asking.
Many companies advertise duct cleaning services. Most charge X dollars per grille or outlet. Prices here range from $7 to $15 per grille. The techniques used vary somewhat, but generally they will employ a vacuum system with long brushes. First, the ceiling (or floor registers) are removed. Then, the vacuum and brushes are sent through the outlet hole. The brushes "sweep" the interior of the ducts and the vacuum sucks up the debris. The vacuum hose and brushes are pushed through the duct as far as possible and then they move to the next outlet. A good company will take your registers and clean them also. They may charge extra for this. If so, while they have them out, you can wash them out in the sink using a mild detergent. After cleaning the ducts, most companies will spray a biocide into the duct to kill any remaining germs and mildew. They don't have to know there is mold in there...if it were my guys they would almost expect it! So, no reason to bring that up, especially if you have had it tested and its not toxic.
Look for a company that is State certified or registered and that has insurance.
Now, the real question is how did the mold get there. Mold needs moisture to grow. The first place it can get this mositure from is the air conditioning indoor unit (air handler or furnace coil). There is a drain pan in this that collects the "condensate" that is a natural by-product of the air conditioning process. The water that collects in this pan is in a cool, dark wet place. Over time, it can turn into mildew and or mold. Its a good idea to have this pan cleaned once a year. You can do something yourself to help, if the drain line coming from the furnace has a removable cap. Take the cap off and pour 1/2 gallon of household bleach down the pipe. Wait ten minutes and then flush with two gallons of hot tap water. This will kill any living mildew or mold in the drain pipe.
The other way "moisture" can get into your duct system is if there is leaks in your ducts. Or, cracks, separations at the joints, etc. If you are really careful, you can inspect the sections yourself. If you find any duct joints that are separated, get a roll of good quality duct tape, clean the area with a cloth and peel and stick the tape on, Make sure to press it on firmly.
In your area, I have no idea what a company would charge for a service call to clean your coils, clean the drain pan and inspect and repair your ducts if necessary. The cleaning and checkout here in our area would cost anywhere from $85.00 to $200 depending in system type and access to it. You may be able to call your local power company for a "free duct inspection". They offer that here in our state and then help the do-it-yourselfer fix the leaks.
I hope I am not giving you too much info! The duct cleaning is well worth the investment. If you can be diligent about changing your air filter every month, the ducts should remain fairly clean for another 3 to 5 years. On filters, try to use a good filter. The "blue mesh" see through filters you can buy for a dollar are literally worthless. They only filter out less than 15% of the airborne particulates. Better to spend $4 or $5 for a "pleated" filter that fitlers out 60 to 90%. These are available at most grocery stores. They will be a little cheaper at a home improvement center like Lowe's or Ace Hardware.
I hope this helps. If you need any other info, write back. Good night.