Krypton was discovered by chemists Morris M. Tavers and Sir William Ramsay who through boiling liquefied air they found trace elements of an unknown element at that time left behind as the other elements boiled away. Because Krypton is usually found in it gaseous state it difficult to pull it from the oxygen, carbon dioxide and other gases in our atmosphere it is mixed with. So scientists turn the air into a liquid and reboil it, so be left with krypton.
An interesting fact about this element is that the name is commonly reffered to the doomed planet of Kal'El. A fictional hero who as a baby was sent to Earth to live out his life peacefully. Unaware that he was affected by radiation from the sun given the extraordinary powers, and donning the symbol of hope for his people he becomes the world famous "Superman". Although this planet is inexistant the creators of "Superman" used the name Krypton because of its meaning in the Greek language.