Question

Which sentence correctly uses a colon? I edited the article and found: comma splices, sentence fragments, and misplaced modifiers. Anna was happy: to go skiing with her sister. Talia decided that: she would accept admission into New York University over Harvard University. I made just one request for the camping trip: I wanted to stay in a cabin instead of a tent. This is what they told me: Because the apartment was too small, and cold for them.

Answer 1

A colon is mostly used to show that you are going to make a list of things after the comma. So, having that in mind, the correct answer is the first option - I edited the article and found: comma splices, sentence fragments, and misplaced modifiers. 
You listed three things here, therefore you have to put a colon. If you are going to mention only one thing, like in the other examples, a colon is not needed.