The public transportation between the main train station and the airport is quite bad indeed. That's because the airport is mainly used for cargo operations.
They might have some special bus for the occasion though, the airshow is quite a big thing.
In any case, remember that the main bus station of the city is at the main square and surounding : Place Saint-Lambert. From there, you can eat, sleep, ask information, and take any bus to anywhere. To go there from the Guillemins train station, you have a bus every 5 min.
Here the map of Liège bus system, but you'll see it's so huge that it might not help you that much (Liège airport is at the extreme west of the map)
http://www.infotec.be/Files/TECLV/NetPl ... ge2006.pdf
A single bus ticket is 1,30 euro. If you have to use more than 1 bus to go to destination, you dont have to buy another ticket.
Finally, if you have a car, concider using it. It's only 1h30 min driving and the parking at liege airport is easy and free.
