I very much doubt there will be any shuttles as these are only usually on for Leeds United matches. The options you have from Leeds train station are the following:
Bus: You can catch the 51 & 52 bus from leeds market (5 min walk from train station) and this will drop you off right outside the ground. The other option is to go to Aire Street (right next to the station) and catch the 229 and get off at the junction of Geldard Road and Low Fields Road. Its a short walk down Low Fields Road then under the motorway bridge to the ground.
If you're getting the bus I would suggest the 229, I get this bus every day and it takes 5 mins to get to the ground.
Taxi: If there are 3 or more this would probably be the best option. Search for Amber Cars (they always have 10 cars parked up near the station) on Google and book one. They'll cost about £5 to the ground. The black and whites outside the station will be a little bit more.
Walk: You're looking at a walk of 30 mins probs. The usual way is through Holbeck but I would suggest following Whitehall Road out of town onto Geldard Road.
Other option is to change trains at Hudds or Dewsbury and then catch the local train to Cottingley. Its a 15 min walk to the ground from here (although Cottingley is a bit rough)