We use a comma + a conjunction (and, but, for, nor, yet, or, so) to connect two independent clauses, as in "He hit the ball well, but he ran toward third base."

Contending that the coordinating conjunction is adequate separation, some writers will leave out the comma in a sentence with short, balanced independent clauses (such as we see in the example just given). If there is ever any doubt, however, use the comma, as it is always correct in this situation.

One of the most frequent errors in comma usage is the placement of a comma after a coordinating conjunction. We cannot say that the comma will always come before the conjunction and never after, but it would be a rare event, indeed, that we need to follow a coordinating conjunction with a comma. When speaking, we do sometimes pause after the little conjunction, but there is seldom a good reason to put a comma there.

I wrote: It is about a grandpa who had died one night but the next morning he came downstairs to have breakfast with his family,the problem was that he did not realize that he was dead.

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The correct form would be: It is about a grandpa who had died one night but the next morning he came downstairs to have breakfast with his family,but the problem was that he did not realize that he was dead. 

 

Source: http://grammar.ccc.commnet.edu/grammar/commas.htm