If no flash is installed and one browses to http://www.plupload.com/example_custom.php it’ll launch a popup box:

How exactly are they doing this? Through some jQuery java-script code snippet or other?
Second, I would like to know if there is a better way to inform the user that they need flash. Or is this an appropriate way?
Check-out SWFObject, it has a utility for checking the current version of Flash installed and if it isn’t new enough or not available at all it can prompt the user to install: http://code.google.com/p/swfobject/
Also if you search Google for
detect flash version javascriptyou will get some other packages/plugins that do the same type of detection.