Some duties might include:
Filing flight plans,
Taking landing fees,
Accepting PPR requests,
Coding Met observations and sending over the AFTN (and other tasks relating to the AFTN),
Taking telephone calls,
Co-ordinating with adjacent units/sectors/agencies,
Strip writing,
Recording ATIS messages,
Passing on urgent messages to the RFFS during emergencies,
Runway inspections,
Making and drinking Tea & Coffee,
Reading MCN cover to cover,
Facebooking,
Playing with all the applications on the iPhone all day.
The ATSA's at my unit have got the last 3 items down to a fine art, we are still working all the other items!
It helps to be able to listen to a sentence once and be able to repeat it verbatim (during emergencies mentioned above), use you own initiative and common sense.
Being able to recognise different aircraft types also helps, again, something else some of ours are working on!