Run-on sentences occur when you have two or more independent clauses in a sentence that are not joined together properly. Once you know how to spot an independent clause and how to join them together, spotting and correcting run-on sentences is fairly easy.
Know the difference between and independent and dependent clause. Basically, a clause is a group of words containing a subject and a predicate. An independent clause is a clause that can stand alone as a complete simple sentence. For example: I went to the store. A dependent clause cannot stand alone, usually because it is preceded by a subordinating conjunction. For example: Because I was out of milk. A dependent and independent clause can usually be joined together in a sentence with just a comma: Because I was out of milk, I went to the store.
To spot a run-on, look for two independent clauses that are joined together with just a comma (which is called a comma splice). This is a run-on: I was out of milk, I went to the store.
To fix the run-on, you can split the clauses into two sentences: I was out of milk. I went to the store.
Another way to fix a run-on, is to use a conjunction: Because I was out of milk, I went to the store. You can also say: I was out of milk, so I went to the store.
The final way to fix a run-on is to use a semicolon, which exists specifically to join independent clauses together: I was out of milk; I went to the store.