For a beginner, perhaps the most important tool to learn is good functional style and abstraction. This code example for a calculator, while not exactly a tutorial, demonstrates these principles. Discussion on the calculator example is located here.
Currently, the ATS site has language tutorials (one for people familiar with ML, and a longer one for everyone else) and several tutorials on library usage. There is also a more dense tutorial or language overview reference that is highly recommended.
Chris Double has written many blogs on ATS. There are also many useful topical tutorials on the ATS site. Of course, there may be resources not mentioned here.
An ATS wiki book exists, but currently only has a few pages.
Other random tutorials:
A debugging tutorial for dependent types.
An example demonstrating [dataviewtype]s.
Anonymous