Hm.. I either don't recognize it, and screw up royally, then realize I must have misinterpretted something, or I just ask the person to please explain again. If it gets to be happening too often, I will attempt to find the cause of the problem.
For example, one of my apartmentmates mumbles, and I have a very hard time understanding his words, so I always tell him he either has to speak louder or speak to me in the same room. When I have an especially hard time, I just tell him "I'm having a hard time hearing speech today" and he usually can speak more clearly for me if he tries. It's an effort on both of our parts.
Another example, I was talking to someone I know online, and I did not understand most of what he said (this time the meaning of his words). He became frustrated with my incessant questioning, and we eventually worked out what the problem was. He has a tendency to be rather vague in his speech, and refer to things without actually mentioning them. This is something I have a lot of trouble with. Once he started to be more concise, we had little problem communicating.
If I have trouble understanding a teacher, I don't like to ask questions in front of the whole class, so I usually ask them afterward, or, even better, send them an email. If it is a reoccurring problem, I will explain to them what I am having trouble with, so hopefully they can help me. I often don't realize I misunderstood something until after I've left the person, and that is why email is so good for this.