How to determine the shift key to decrypt a ciphertext which was encrypted using Caesar cipher?
There are only 26 possible shifts with the Caesar cipher, so you can check them all pretty quickly with a computer, or by hand for fun.

You could also get one step more sophisticated and do a frequency analysis: make histograms of ciphertext letters and compare those to the frequencies of English (e is the most common single letter; followed by t, a...just remember Etaoin Shrdlu and you'll be fine). Then you can do a $\chi$-squared test to compare your ciphertext frequencies to the expected ones from English.



Usual warning: because of how easy this is to break, make sure you only use it for fun: it offers no real security. Here's a longer discussion about cracking ciphers by hand.