When teaching intermediate-level students how to become better listeners, we often advise them to listen for differences in intonation or word choice that might signal meanings that are different from the dictionary definition of the words themselves. Learning to make inferences or to infer meaning from the way people express themselves in a foreign language can be daunting.
Some of my students who don't recognize the word sarcasm have difficulties understanding it from a written definition, so besides using examples from their textbook, Listening Power 3, I offer them some free online examples linked to my wiki. It is helpful for students to be able to listen to audio tracks or video examples outside of class.
The first one here is from the BBC's Learning English website. It gives a student some insight into English or British culture and a few audio examples of what sarcasm sounds like. The next is a link to a popular American TV series called The Big Bang Theory (TBBT). In this segment of an episode, one of the main characters Sheldon is trying to learn what sarcasm is. This video clip reinforces the explanation given by the BBC.
Personally, I'm not a fan of sarcasm as it was not part of my personal background. I didn't encounter it much until I was in high school. As explained in the BBC Learning English track, not every culture uses sarcasm as a form of humor. When dealing with non-native speakers, especially, but also with native speakers of English who you don't know well, be careful about using sarcasm. If the person you are interacting with doesn't know that you're being ironic or sarcastic, (s)he could misunderstand you and be hurt by your words. Sarcasm when aimed at a person unfamiliar with this form of communication can feel like an insult or a put down.