PSP said it best. An automatic tranny uses a torque converter to transfer engine load to the drivetrain. A manual transmission uses a clutch.
Here's a good introduction to auto trannies:
http://auto.howstuffworks.com/automatic-transmission.htm
There's a manual tranny page there too if you search for it. Read up on all of that.
Tiptronic is just an auto tranny that shifts when you tell it to. It still has all the deficiencies of an automatic tranny.
F1-style transmissions use a hydraulic system to operate the clutch instead of your foot on a pedal doing the same thing. In essence, it's still a manual transmission. That's over-simplified of course, but there's the basics.
DSG of course, is a lot different.