This page has several ways for programmers to get started with Squeak.
For non-programmers, see Squeakland.
For WebWareWriters, see Seaside, it'll change the way of your Squeak life;) It's well documented and easy to learn. (–Jigme, China)
Squeak.org tutorials - There are several tutorials listed in the documentation section of the Squeak.org homepage, including Work in progress's BankAccount tutorial, etc.
Squeak Development by Example by Stephan B. Wessels. Updated for Squeak 3.5. Introduces SqueakMap, SUNit, Skins and numerous other goodies as well as a complete walk-through of Squeak development exercise.
Self Study Course a guided tour of Squeak. (detailed explanations, useful but unfinished)
Making OO Smalltalk - A beginner's introduction to Squeak by Jason Steffler. It is geared toward Linux, but is useful for learning Squeak on any platform. (WARNING – this reportedly does not work on recent Squeak's.)
(To the tutorial authors: Please include the Squeak version number which your tutorial was written to work with. It's okay if your tutorial doesn't work perfectly with the latest Squeak, as long as it works well with a named (non-alpha) version of Squeak.)
Squeak learning resources on the Internet:
Various tips from Mark Guzdial, author of a text book based on Squeak.
Squeak el Smalltalk del Futuro [1.07 Mbytes, in Spanish] by Antonio Fuentes Bermejo. An introduction to the development of MVC and Morphic applications (130 pages in pdf format).
Notes and lecture slides on the Squeak environment from University of Washington's undergraduate programming languages course. Targeted towards getting you coding quickly. Assumes you have a supplementary text or instructor to teach you the Smalltalk language properly.
RedFigure Tutorials Tutorials for making stuff in Squeak without a previous knowledge of programming concepts.
Squeak Help by Maarten Maartensz, who doesn't believe in Swikis.
EasySqueak A package to develop Squeak training materials
Exercises
Ultimately, to learn Smalltalk, you have to spend some time programming in it. The below exercises make terrific practice.