Verbal irony is when what is said is the opposite of the literal meaning.
1. Sarcasm. In sarcasm, the speaker says the opposite of what he or she means in order to show contempt or mock. The speaker's tone may vary, so it is important to try many different 'voices' when reading. Not all sarcasm is delivered rudely or angrily, some is more light-hearted and can even sound friendly.
2. Overstatement or exaggeration. A really good example of this (and one that you have probably heard) is misusing the word 'literally.' Many people use 'literally' in conversation, such as, 'I literally died.' Well if you're alive to say this, then no you did not. This kind of exaggeration is another example of verbal irony.
3. An understatement. This is when a person minimizes something, making it seem less important than it really is. A good example of this that you've probably heard is 'no big deal.' This is usually following a description of a great feat, such as, 'I just wrote a 10-page paper in two hours. No big deal.'