Can you provide some more information about your car, i.e year, engine, transmission, etc.?
Sounds like a low idle issue to me. To test this, try starting your car in neutral (i assume it's manual?) and just leave it running without touching accelerator or anything else. If it cuts out when doing this, I would say it is a low idle issue.
To fix this the first thing I would try is doing an ECU reset. The procedure is outlined in this thread: http://www.alfaowner.com/Forum/alfa-...acle-cure.html
If that does not help, then you may have a problem with your idle actuator/throttle body. They're not particularly cheap to replace, but you should be able to pick up a second hand one from a wreckers for about $100-150 AUD. From what I understand, there are two different types of throttle body's one for selespeed and one for manual. The manual one is the more expensive one (of course :S).
Some people say you can try giving your throttle body a clean, but i've heard this often causes more damage than it fixes.
This is just my guess, don't know if it's right. Let me know how it goes.