DIAGNOSIS The microwave is drawing more current than the circuit can handle, which points to either an overloaded circuit or, less commonly, a short inside the microwave.
FIX First, check what else is on the same circuit. Unplug or turn off other appliances on that kitchen circuit (toaster, coffee maker, etc.). Try running the microwave by itself. If it no longer trips, the circuit was simply overloaded. You'll need to run the microwave on its own dedicated circuit or be careful not to run other high-wattage appliances at the same time.
IF THAT DIDN'T WORK If it trips the breaker even with everything else off, the problem is likely in the microwave. A failing magnetron (the part that creates the microwaves) or a shorted component can cause excessive amp draw. This requires professional diagnosis and repair.
HEADS UP Never just keep resetting the breaker or use a higher-amp fuse. That's a fire hazard. You need to resolve the root cause of the overload.