The alternator belt on a 1994 Eclipse is replaced by loosening the alternator bolts, moving the alternator downward, and slipping the belt off. A new belt is then routed around the other accessories, placed on the alternator, and the bolts tightened.
It sounds like it could be an alternator problem, the easiest way to determine this is to disconect the battery while it is running, if it stalls, or bogs out, replace the alternator. ( but it could just be faulty wire conections. ) hope this helps.
You have to find the alternator then look at where it is connected to the motor there will be a slide mechanism that you will have to loosen which will release the slack on the belt so you can get it off.