When to use a comma after "but":
* When it connects two independent clauses. This means both parts of the sentence could stand alone as complete sentences.
* Example: "I went to the store, but they were out of milk."
When NOT to use a comma after "but":
* When it connects a dependent clause to an independent clause. This is when the part after "but" needs the part before it to make sense.
* Example: "I went to the store but couldn't find the milk."
In short, use a comma after "but" if the sentence is two independent clauses joined together. If it's a dependent clause followed by an independent clause, no comma is needed.