The granite tile fell off of our fireplace, how do we put it back on.

Here is an article that might be helpful - https://www.thisoldhouse.com/how-to/how-to-tile-fireplace-surround - good luck

What was the granite applied to? backer board, drywall, or brick fireplace?

Ophs cut that one off? was the surround built up with concrete before the granite was applied? are they 3/4 slabs or tiles? is it set in thin-set or is it applied with adhesive like silicon, liquid nails or mastic?

https://www.youtube.com/watch?v=q-44C601Om4 here at 3:31 you can see them beginning to apply thin-set to the previously prepared fireplace which was brick that they applied wire mesh too and created a base of concrete for the new granite surround, Here is right kind of thin set, https://tilesgraniteltd.wordpress.com/2013/02/14/black-granite-tiles-on-fireplaces-what-is-the-right-adhesive-to-use/

At 2.54 you can see this guy using mastic to apply tiles to a surround, and how you back butter the tile and apply to wall... https://www.youtube.com/watch?v=QS1rPSO-XCQ If your repair is a tile I would use Mastic (adhesive) get gray. Larger and thicker side slab, I would use thin-set. Both will require a small trowel with teeth, check your product to see the size required. I would first use a chisel to remove as much of the old product as possible first from the surface it was on . Apply mastic to wall, and back butter tile. Once in place, use a level to make sure it is level, and flush to surfaces touching, and I would use painter's tape to hold in place for the day.

Scrape off any adhesive in the area. Use a concrete construction adhesive in a caulk tube and stick it back on. Use tape to hold it in place as the glue dries.

backer wood, the cement is all stuck to the 1/2" granite tile, will that have to be removed prior to putting on a special glue