We traveled by Ryanair to Haugesund (actually Helganes) airport in September 2005. When I was planning this 'off-season' trip, I found it difficult to find information for costs, schedules, and options after the tourist season ended August 31.
I have placed the following information in a travelogue under Stavanger, Norway (as it was our base). It includes prices, schedules, and travel times for three weekdays:
Helganes (Haugesund Airport) to Kopervik by taxi
Kopervik to Stavanger by ferry
Stavanger to Tau by ferry
Tau to Preikestolhytta by bus and taxi
Preikestolhytta to Tau by taxi
Tau to Stavanger by ferry
Stavanger to Haugesund by ferry
Haugesund to Airport (Helganes) by taxi
(Stavanger to Lysefjord / Lysebotn option)
By airplane to Sola airport is probably the best way. Connections to Copenhagen, Amsterdam, London and a few other British cities, and Bergen and Oslo. Airport bus to the city centre.
Ferry to Newcastle, bus and boat to Haugesund and Bergen. Bus to Oslo and Kristiansand.
Trains via Kristiansand to Oslo. From Kristiansand or Egersund you can take the ferry to Denmark.
In the city centre you should walk. Most of it (the best parts) are closed for cars, and besides it's not really THAT big. For travelling to other parts of the city, there are buses to all parts of Stavanger from the bus station or from outside the Cathedral. Fares are usually around 20 NOK. If you wish to go to Sandnes or further south, the local train system has departures every 30 mins to Sandnes and every 1 hour through Jæren to Egersund. 25 to 80 NOK depending on how far you're going. If you're going to the islands or to Ryfylke there are boat to most of the islands and to Ryfylke as far as Sauda, and ferry to Tau. The sightseeing boats such as Clipper are also good experiences. The Nordsjøveien bicycle route from Stavanger to Egersund is a popular nature experience.