You can find the schedule for buses Linea 9373/A–Linea 9373/R (Alghero–Fertila Aeroporto) on the airport's website. These buses will take you directly to the city. Tickets can be purchased at special machines located in the airport. A ticket is valid for exactly 90 minutes from the time of validation and allows unlimited transfers during that period.
Depending on the type of ticket and number of trips, prices vary: a single ride — 1.30 EUR; 12 rides — 13 EUR; a day pass valid until midnight — 3 EUR; if you buy a ticket from the driver, you pay 1.70 EUR.