I did a lot of this homework about 2 years ago for my TDI (apparently, 2001 TDI's are not OBD2 compliant...)
So let me offer some specifics:
App - GO on google play and download an app called "Torque Lite" -, its the free version of "Torque" - and will do everything you need for scanning codes (and more...)
dongle : I like this one :
BAFX Products® - Bluetooth OBD2 Reader for Android
by BAFX products. It works on every car I've tried it on (my '01 TDI, 2013 Honda van, '09 Kia, '01 Dodge truck) If you dig deep you'll find that there are 5 or 7 different protocols that could be used by an OBD2 compliant vehicle - this one grabs them all. (some cheaper ones dont...).
The BAFX dongle uses bluetooth, Torque uses android, if you have an iphone or an android phone without bluetooth(???) I cannot help you. I'm sure that there are similar apps for iphone, but I cant vouch for any.
To actually scan codes, plug the dongle into the car, turn the key on and tell your phone to look for bluetooth devices - after a bit it should find one called "OBDII", pair to it (i think the code is 1234...it says in the papers that come with the dongle) then run the torque app. I think that torque will work out of hte box, but you might have to go to the settings page and tell it to use the 'adapter' called "OBDII"
There is a 'scan codes" button when you first run torque - that'll tell you what its saying.
Hope this helps.
-John