One thing to note, the Enigma's encryption algorithm is pretty good, but not perfect. One weakness is that a letter can never be encrypted as itself which eliminates at least on character and can make it easier to crack. Most of the issues the Nazi's had that made it crackable had to do with their processes as they used the machine. Key exchange is hard in a system like this where you don't really have an out of band method to exchange keys.
If you want a detailed description of how Enigma machines work check out the Wikipedia article( http://en.wikipedia.org/wiki/Enigma_machine ), or the many other articles on the internet, I'll just give a quick overview here.
The Enigma machine basically consisted of three or more rotors that had contacts on both sides. The rotors are set to the encryption or decryption "key" then a button is pushed which goes through the wiring in the rotors, then lights up a lamp corresponding to the encrypted output (there's a lamp for every letter in the alphabet). To decrypt you simply start with the same key that was used to encrypt the data and type in the cipher text. One thing significant about the Enigma machine is that the rotors rotate as each key is pressed, so the encryption key essentially changes with each character.
I was in a thrift store recently and saw a game with a screen and a keyboard and I thought, that would make a good Enigma machine (I've always wanted one, but I know my wife would kill me if I bought a real one $$$). In this instructable I'll show how I gutted an kids game and used an Arduino to hook up to the keypad and speaker. The code's not too bad (so far). This version is a simple three rotor Enigma machine. You can switch the rotors around and change the letters for the rotors. Future plans are to all for more rotors, allow changing out the reflector, allow for spinning the ring around a rotor, and a plug board implementation. This Enigma machine will be able to encode and decode messages to and from the real, old Enigma machines used during Wold War II.
Note: The image for this page is from the Wikipedia article on Enigma Machines