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You need at least a 68020 (a Mac II or LC, for example) to run AppleScript 1.1 or the newest Apple's G5.
AppleScript is basically two parts: a script editor that you write scripts with and an AppleScript extension or component that handles the execution of the scripts themselves. Your computer should include both tools: AppleScript installed as an osa component (as well as QuickTime or SoundManager should be installed) and an applescript editor (you can find Apple's Script Editor within your AppleScript folder).
AppleScripts can be run in a bunch of ways: from a script editor (such as Apple's Script Editor, Satimage's Smile or LateNigth Software's Script Debugger), from an applet or droplet (a script saved as standalone application) or from a third-party application (script menus, launchers...).