What is a comma splice and how can I stop doing it?

Michelle ran to the car, Brian chased the robber.

The sentence above is incorrect. 

Michelle ran to the car is a complete sentence, and Brian chased the robber is also a complete sentence. To join them with a comma, you need the word “and” or some other coordinating conjunction. If you just put a comma between them, that's an error called a comma splice or a comma fault. 

Quite simply, a comma splice is the attempt to join two independent clauses with a comma, but without a coordinator.

Let's look an example of a comma splice and how to fix it. 

Comma Splice - I got up late this morning, I didn't have time  for breakfast. 

Correction - I got up late this morning. I didn't have time for breakfast (Full stop used)

Correction - I got up late this morning; I didn't have time for breakfast (semi-colon used)

Correction - I got up late this morning, so I didn't have time for breakfast (comma and 'so')

Correction- I got up late this morning, and I didn't have time for breakfast (comma and connective)

(source: http://grammartips.homestead.com/splice.html)