The document discusses avoiding run-on sentences by correctly connecting independent clauses. A run-on sentence incorrectly connects two independent clauses without proper punctuation, such as with only a comma. There are several ways to fix a run-on sentence, such as using a period to separate into two sentences, adding a comma and a coordinating conjunction, or using a semicolon. Special care needs to be taken to avoid run-ons when a pronoun refers back to a noun in the previous clause, when there is a suggestion or directive in the second clause, or when clauses are connected by a transitional expression.