Right, so, mics are delicate but they're not made of wafer-thin glass :) Here's some things you can do to clean up your mic:
-Any grilles or screens can be taken off and given a nice wash in warm water, then rubbed with isopropyl alcohol to make sure it's completely dry and princess pretty.
-If you have a capsule-type mic, take the capsule off and wipe down the contacts with a slightly damp alcohol-soaked cotton swab.
-You can clean the diaphragm, just be careful. I've used damp swabs, but I've been told for more delicate mics, use a little cheap paint brush, stick it into a stream of steam coming off of boiling water or a teakettle for a few seconds to get it damp, and then gently brush off all dust and schmutz. Read this linkydo for good info. He brings up the point that some old mics use PVC in the diaphragms, so know what you're working with before you dive in. If your diaphragm is in serious trouble, it should be replaced professionally. You'll know if this is the case - it should sound terrible.
-Down on the connector side, your XLR can get pretty nasty. These are pretty easy just to replace. There's a little screw holding it in - take it out. These are just the connector portion of any XLR cable connector. A little solder and you are set. If you're not comfortable with soldering, there are crimp and screw down terminal connectors as well, although soldering will be the best way to preserve the cable length that may be a bit precious.
-I regularly use CAIG Labs DeoxIT to keep the XLRs in good shape. Just squirt in a little bit, then use an XLR cable end to work it onto the pins and wipe up any excess. I would ask the rental/borrow department at the school to make this part of their check-in process.
And, of course, if it ain't broke - don't clean it!