Is fish countable or uncountable?

Fish has the same form in the singular and the plural. When you are talking about different kinds of fish, fishes can be used.  

• There are fish in the pond.  
• I think the tiger fish is the most dangerous of all fishes. 

Fish as a countable noun 

Fish is a countable noun when it means an animal that lives in water and has gills and fins.  

• an ocean/river/sea fish 
• How many fish can you catch? 
• He landed a lot of fish yesterday.   

Fish as an uncountable noun 

Fish as an uncountable noun means  the flesh of fish used as food. Fish and other sea creatures such as lobsters, crabs are called seafood [uncountable nouns].  

• dried/frozen/smoked fish 
• Do you eat fish and chips? 

You cannot make fish plural or use with the indefinite article (a).  

• I am having fish for dinner.  

Not I am having a fish...