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Probably the best approach to learning AppleScript is to buy one of the available AppleScript books and reading through the scripts in the book. Constantly experimenting with AppleScript also helps. Because Apple event and object model support in third party applications isn't always consistent, you will quickly discover that what works in one program may not work in another. Experience is the best teacher in these cases.
There are a number of internet resources available. Check out the links on our AppleScript Links page to get started.
Another way to learn to script is to study the scripts that others have written. Look at any and all example scripts that you find. You can also watch the progress of Apple events in the Log window (AppleScript 1.1 and up) to learn more about how scripts work. If you are using one of the third party script editors (Scripter or Script Debugger), you can watch variables as they change in debugging mode, and step through scripts to see what is happening and what might be going wrong.
If you are working with an application that is recordable, you can record actions in the application and then study the scripts that it produces. Since the application is "writing" the script, you will get a better idea of the commands that it understands and how they should be scripted.
There are also tutorials and help modules available for download at Apple's Official AppleScript site.
Of course, you can always join the MACSCRPT or AppleScript mailing lists, download and examine scripts from ScriptBuilders, and read the scripts posted on our BBS. Read all of the messages, and run some of the scripts that are posted and discussed. This is a bit more interactive than reading a book and offers the advantage of often immediate feedback from other scripters.