When you have a sarcastic sense of humor, people can find you a real curiosity. It can be hard for some people to tell when you are really joking. You rarely say exactly what you mean, and there's an edge to sarcastic humor that few people can truly appreciate. Your straight-faced delivery and dry cynicism will either leave everyone laughing or have them wondering what they missed.
Watch your delivery when speaking in order to have a sarcastic sense of humor. Deliver what you consider a joke in a monotone voice as if it is more for your own amusement than for anyone else.
Show that you have a sarcastic sense of humor by being the opposite of a typical jokester. You are not looking for a laugh to prove you are funny. You avoid easy punch lines by making statements that require others to think for a moment before "getting it."
Make your statements without showing others what parts are in fact funny. This is why those with a sarcastic sense of humor keep a straight face and monotone voice in their delivery.
Add a tinge of mockery and a condescending attitude when making your sarcastic remarks to others.