It's those internal conversations, those inner thoughts that often give the reader insight into your character's soul. There are two ways to approach this: the indirect thought and the direct thought.
With the indirect approach, the character's thought is more of an observational commentary. For example, if you are writing a story about a child waiting to be picked up at school, you might write: The boy worried that his mother may have forgotten him, or worse...she may have had a horrible car accident. This is an indirect character thought because you did not write the exact wording of the character's inner dialogue.
A direct character thought is written as internal dialogue. Some authors use italics to signal that the words are the character's thoughts. Using the above scenario, you might write: Billy sat on the steps outside the gymnasium. The schoolyard was quiet. Maybe Mom didn't see the note I left on the table. Or maybe she had one of her episodes. Last time that happened Dad yelled at her, said he didn't want her driving anymore.
When writing direct thoughts do not use quotation marks. A tag, such as he thought, is optional.