There are three main ways to correct a run-on sentence: 1) Separate the two ideas into two sentences with periods, 2) Add punctuation such as commas and use FANBOYS conjunctions to connect the two sentences, or 3) Use a semicolon to join two closely related sentences without it being a run-on. The document provides examples and exceptions for properly using semicolons and FANBOYS conjunctions to connect or separate ideas in run-on sentences.