Manchester is geographically the closest airport. From there trains take between 90 minutes and 2 hours, depending on the exact train taken. Some require one change at Crewe, some require one change at Manchester Piccadilly, some require more changes.
Anytime tickets are about £25 (as at May 27, updated prices still to come).
The train station is well sign-posted, but you may need to exit the building to get to the "sky way" to get to the station.
For options other than Manchester Airport see Travelling by Air.
Next: Travelling by train