If you are travelling on a package holiday or you are sleeping on a good quality hotel of the region, ask your tour operator or your hotel for free shuttle service from the Goa Airport to your destination.
If this is not you case, check out the other options that you have.
There is a pre-paid taxi booth outside the terminal. Try to use a pre-paid taxi from the booth to reduce the chances of you being ripped off. The typical fare to Panaji city center is INR 800 - 900 and the trip takes 40 minutes.