Sorry about the delay in posting. I do not doubt that it will happen again in the future, unfortunately. Anyway, let me begin.
Writers do not have the luxury of text in nice, neat thought bubbles. We leave that to cartoonists (no offense to them). In literature, it's a tad more complicated to display thoughts. It can be done in a few ways.
First-person stories use thoughts in the most dynamic, fun way. Thoughts are thrown in along with the rest of the text. The narrator generally breaks in with his or her thoughts frequently and may tell jokes or propel a tone that is nearly impossible to replicate in other POVs.
Quotes may be used for thoughts, with the discretion that the dialogue tag should reveal that the character is not speaking aloud. Sometimes characters may murmur things along with thinking them, especially if they have something important to state, yet cannot have their thoughts heard because of the POV.
While used infrequently, at least to my knowledge, italics can convey thoughts as well. Robert Jordan does a splendid job showing the thoughts of his POV characters mixed in with the text like that of first-person, albeit italicized.
Character thoughts are an important part of any story. While they are not necessary, they help to establish a tone in the writing, can be used to establish characters (and keep them from being flat), and can foreshadow as well as anything else.