There is a direct bus, which departs from Stop 13 Henley Beach Road - North side and arrives at Stop 1 North Terrace - North side. The services depart every 20 minutes, and operates every day. The journey takes approximately 30 minutes and costs around $4.
A taxi will cost approximately $30 and take around 10 minutes. There are taxi stands conveniently located at the airport exit.
There is also the Adelaide Airport bus services. Out the front of Adelaide Airport there is bus stop 10 at the front of the terminal, which will take you to the city.
For further details, see Transport.