Sarcasm (noun) is to say the opposite of what is happening at the time. It is as a type of humour, usually used to make fun of someone. For example, you see your co-working sitting down reading the newspaper and drinking coffee, so you say: 'Wow! You look really busy!'
Obviously, your friend is not busy - you were being sarcastic (adjective) as the opposite of what you said is true. Your co-worker would probably feel embarrassed by what you said and other people listening might laugh at your sarcastic joke.
For example, your friend says 'I think that London is the capital of England.' Now, everyone in the world knows that England is the capital of England, so your friend has made a very obvious statement. This is a great opportunity to use sarcasm. You could say:
Friend: I think that London is the capital of England?
You: Is it? Wow! You are really intelligent!
Imagine that someone has done something wrong or made a made a mistake; for example, your friend took a test and got a really low score. Time for some sarcasm!
Friend: I only got 15% on my history test.
You: Well done! I'm very impressed!
When you get some bad news or when something bad happens to you you can use sarcasm:
For example, when you drop your cup of tea on the carpet you can sarcastically say Oh, great!
Imagine that your friend went to a business job interview wearing shorts and a t-shirt. You knew that he would never get a job dressed so casually.
Friend: I didn't get the job; I failed the interview.
You: What a surprise!
Note: Because sarcasm can hurt peoples feelings, you should be careful when you use it. Don't use it too much and don't use it on anyone who might punch you on the nose!
Intonation is as important part of sarcasm. To help you out, watch the following clip and pay attention to the sarcastic intonation of the man on the right: