Or if it's a single command, like 'purge', simply use this AppleScript command:
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The same way you'd do it in any other AppleScript. If you're looking for a tutorial on writing AppleScript and hooking it up to buttons, you should search for that using a search engine like google.
If all you want to do is run the 'purge' command, you don't need a button for that. Enter the command I posted above. Save your AppleScript as an application. To purge memory, launch the application. Every time the application is launched, it purges memory. No button needed/
If you want to do other things, like present a dialog, there are AppleScript commands for that. Google search terms:
applescript dialog.
If you want a complete window, with multiple buttons, one of which purges memory, and other buttons that do other things, look for a tutorial on making windowed applications with buttons in AppleScript. Everything other than
do shell script "purge" will be common to all such AppleScript apps.