Quebec City Airport

There are regular flights to Quebec from other Canadian cities and other international airports. However, there is no bus or shuttle service from Quebec airport to the city center. However there have been propositions to provide such a service in the near future. This leaves you with two other options

Taxi and Limo service. 

Taxis run a flat rate service from the airport into the old town for 32 dollars. If you are not going as far as the city center it can be cheaper just to let the meter run. A Limo service can also be arranged from the airport.

Car hire

Another option is to rent a car for the duration of your stay. This gives you more flexibility to tour around the area at your leisure and can work out cheaper in the long run.