If you are referring to the number of individual shrimp, you use many, because they are countable:
"How many shrimp can you eat?"
"I can eat ten of them."
(Note that the plural of shrimp is both shrimp and shrimps. Either can be used. It's probably a bit more common to hear the singular form.)
If you are referring to shrimp in a general way, you use much:
"How much shrimp can you eat?"
"About a pound."
Note, however, that these are not absolute rules when it comes to idiomatic speech:
"How many shrimp would you like?"
"I'm having company over, so give me five pounds worth."
"How much shrimp would you like?"
"I can probably only manage five of the big ones."
So, while there is a general difference between much and many, where one is more common in a particular context, both can be used and understood.