(These steps worked on my 95 C220, I think that it should be substantially similar for your '99, as they're both W202s. But if anyone has better information, please correct me)
Really wish I had a digital camera to help step you through this process.
First, place a drop cloth on the passenger footwell floor to catch any falling screws or dirt.
Look on the passenger front side footwell.
On the left hand side of the footwell, there's an air vent. Remove that. (I think there's a plastic phillips-type connector that you need to turn)
Then, on the top of the footwell, there's a large plastic panel that you need to remove. It has three phillips screws that you need to take off to get this panel off.
After removing this panel, look up (a flashlight might help). There should be two compartments that are secured by clips. The long skinnier one is the cabin filter. (BTW, it might be a good idea to change this at the same time that you change the blower motor- this might eliminate the problem-- at the very least, you'll have a clean filter in place)
The squarish one is the blower motor assembly. unclip the cover (I think there are 2 or 3 slide-type clips at the front), and there's the blower motor. It unscrews out (I think that there's 4 torx screws, but they might be phillips- if its torx, I think that it's a T-23 or T-22 size one- Allen keys might also work) and there's a single electrical connector that you disconnect and there's your motor.
When you have it out, might not be a bad idea to reach in and clean out some of the crud in the general area.
When I cleaned out my blower motor, a toothbrush was very helpful in getting grit and grime loose.
If you reconnect the motor after cleaning and don't have any noise when it's spinning, *retest* it when it is back in its cavity before sealing it all up-- you might find that it makes no noise when you're holding it in your hand, but it will make noise when it is back in the hole.
Worst case is after all this, if it still makes noise, you know how to put in your new motor without going to the dealer.
Note: Be very patient when you're working with the clips for the first time-- the first time I did it, I swore more than a civillian should during peacetime.