From the airport to downtown by Flybussen
On arrival at Stavanger airport Sola, proceed through customs and into the arrivals hall (~20 mins). Immediately outside the arrivals hall, find the airport shuttle "Flybussen". It is the least complicated way to get to town. It leaves approximately every 20-30 minutes and the trip takes about half an hour. The one-way ticket costs 179 NOK and the return ticket costs 264 NOK if bought on the "Flybussen" webpage. The ticket can also be bought by cash or credit card on the bus by paying an extra fee.
The driver will speak English and will be able to inform you of when to get off for your hotel.
Your Flybussen ticket entitles you to one change onto the local buses.
From the airport to the UiS campus by Flybussen
The instructions are essentially those to go to the Stavanger center. The difference is that only the Flybussen buses going to Stavanger center "via SUS/UiS" cross the campus. The most convenient stop is UiS Øst. The buses leave the airport every hour.
Travel from the airport by Kolumbus buses (cheaper, but longer option)
For the travel from the airport, also the buses by the Kolumbus company (that operates the public transport in Stavanger in general) can be used, but there is no direct bus and the travel takes about one hour. The timetables can be found at the Kolumbus webpage or also at Google maps. The tickets can be bought via the Kolumbus app at the prices indicated here. The single journey ticket can be bought directly from the bus driver only in cash with an extra fee. With a valid Kolumbus ticket in the app, one can also use the city bikes for 15 minutes for free.