Mark
All sations a adistance away from Farndale, Only the summer moorsbus services run into Farndale itself but Bus connection are possible to Kirkbymoorside our local town and on a less frequent basis to Hutton le Hole.
There nearest mailine station is York although this is over 25 miles away. Malton on the scarborough line is nearer.
Nearest is probably, Castleton on the eskdale line although there are no but there are no bus connections to get you nearer.
There are regular bus connections from York to Helmsley / Kirkbymoorside 31/31X and from York and Malton to Pickering 840.
From Scarborough via Pickering to Kirkbymoorside and on to Helmsley is served by the 128.
A host of other buses run on particular days from Malton, Helmsley and Pickering to Kirkbymoorside or Hutton le Hole which is probably slightly nearer to Farndale, but these are mostly on a one aday basis. 174,176, 177, 178, 179, 196, 199 to check for details the following website is useful
http://www.northyorkstravel.info/ryedale.php
To complete journey you will need a taxi unless cycling or up for an approx 8 miles walk.If staying in Farndale ask where your staying for advice.
During the daffy season (April) a shuttle bus service runs from the hutton le hole car park at weekends and through out the summer there is a Sunday moorsbus service into Farndale itself. Again this is on a fairly infequent basis.