With applescript, unfortunately they only let you do so much before you have to jump into some development program and create a special UI application just for the applescript.
The basic overview:
Mac Automation Scripting Guide: Prompting for a Choice from a List
With the basics arsenal you can at least create some kind of advanced ui by using perhaps a series of pop-ups.
As williamadowling points out, the most convenient way is to use ExtendScript's ScriptUI. You find the reference documentation by Peter Kahrel at ScriptUI for dummies | Peter Kahrel
If you want to do something that applescript can do and not extendscript, from extendscript, do not worry- there are ways to use your jsx UI and then later execute an applescript.