Forgive me - is it near the train station?
I would go by train from York...
It's a couple of miles out of town in the ex-industrial part of Sheffield called Attercliffe.
If you come in to the train station, then I'd recommend getting a tram into town from the station tram stop (ones marked Cathedral, Malin Bridge or Middlewood) and get off at the first stop called "Ponds Forge", then jump to the opposite platform and catch another tram going towards "Meadowhall".
Get a ticket called a Dayrider and you'll get all the journey's for one price.
The stop to get off at is "Attercliffe" (takes about 15 mins).
Get off there and it's about 5 mins walk to GFE. If you've got Google Maps then I usually walk down Chippingham Street and turn left on Worksop Road. GFE is on the left hand side just before you get to the Attercliffe Road. (8-10 Worksop Rd, Sheffield, South Yorkshire S9 3TJ). The entrance is at the rear (fnarr fnarr).