Replace the comma with a semicolon, which is meant to join two independent clauses. "She was very tired; she went to bed early."
Use a period to turn the two independent clauses into two sentences. "She was very tired. She went to bed early."
Add a coordinating conjunction after the comma. Coordinating conjunctions are words that can join two clauses. The seven coordinating conjunctions are "for," "and," "nor," "but," "or," "yet" and "so." Choose whichever of these words works best in your sentence. "She was very tired, so she went to bed early."
Include a subordinate conjunction in the sentence. Subordinate conjunctions are words such as "although," "because," "since," "while," "if," "whether" and "whereas." By adding one of these words to the sentence, one of the clauses becomes dependent upon the other and the comma is no longer incorrect. "Since she was very tired, she went to bed early."