Getting from Wrocław airport to Książ Castle, near Wałbrzych

Can anyone advise me on the best way to make the journey from Wroclaw airport (arriving afternoon) to Kzias Castle, near Walbrzych. Public transport or taxi? What sort of cost are taxis in Poland? Any advice would be much appreciated - thank you.

Taxi would be of course most convenient - but the cost may be approximately 250PLN.
Another option would be train from PKP Main Station to Walbrzych Miasto, and then bus #8 (from Armii Krajowej Street) directly to Ksiaz Castle.
You may also go to Swiebodzice town from Wrocław (Bus or train) and take a walk to the Ksiaz...
Several other options yet - more or less acceptable.

How long does it take to get to the castle from the airport? Is it possible to rent a car and drive there? (I do not speak or read Polish)

I would say roughly an hour. Once you left the industrial estates around Wrocław behind you - plenty roundabouts - it is an easy and pretty scenic road.

Zamek Książ is pretty well signposted - it is on the right side after you have passed Świebodzice. It is on a dual carriageway going into Wałbrzych.

Expect traffic jams because of ongoing road works into town .

Would love updated info on current taxi fare costs!

no idea about taxi costs, but you may check out this website:
funtrips.club

He will probably drive you there and even to more places to see....