What do you put in a story when someone is thinking?

There are various ways to handle this, but one thing you don't need to do is to enclose the thought in quotation marks. You could write the thought in italics.

Example: He considered the situation. If I try to make a break for it, the dog will bite me.

You could also write the thoughts without italics, as long as it's clear to the reader that someone is thinking. Sometimes a writer might insert that information in parentheses.

Example: He considered the situation. If I try to make a break for it (he thought), the dog will bite me.

The important thing is to make sure the reader is never confused.