The important thing to note is that there are two UI frameworks which have some apparent overlap. One in flash, the other in Flex. In order to use flex, you'll need the Flex SDK. The Flex SDK is free, but flex builder is not (The IDE adaptation of Eclipse.)
Really flex is just a set of libraries and frameworks in as3.
Most of the packages are in the namespace "mx.", and even though the component names are the same (Button in flash, Button in Flex) flex has a much more robust framework.
You will also increase the size of your swf file by 30 to 50k, but if you are looking for robust UI, it's well worth it.
I'd also recommend learning how to use the ResourceBundle and CSS capabilities of flex, as localization and skinning are much simplified by the use of both.