You can download a free trial of their software or you can view an online demo on the amember.com site.
As far as phpbb3 is concerned you replace the phpbb3 registration screen with amembers (code supplied with mod (I also replaced the phpbb3 request new password link to reference amember)).
The one thing I really like about the amember scripts is that once you have set it up the whole process is taken care of for you ie payment collection, moving members to the appropriate usergroup once they've paid or not if they don't, reminder emails etc.
On the down side I found the only way I could import my previous subscribing member into amember was manually but that might have been because I tend not to read the manual (man thing
) as I think there is a script to do it.