Teaching Turing, by David A. Mellis and Aram Armstrong is an easy to understand, fun environment for learning about and programming Turing machines. The goal is to show people how Turing machines work by having them program a Turing machine themselves.
The structure of Teaching Turing is divided into a series of levels with the earliest stages very clearly walking the user through the basic controls of a Turing machine, then working up to a series of graphic puzzles solved through programming. Users can move at their own pace through the levels, or proceed to free exploration and programming of the machine.
PDF describing Teaching Turing.
Related: A train that can calculate, the Cut-Out computer.