I'm not sure how to fasten the frame of an iron fireplace frame to the stone of the fireplace. What type of fastener would work best in this application? I want to bolt the frame to the stone?

ive not had to do this often but when i did i used the lead insert type of lag screw... it involves drilling holes into stone then putting incert in then bolt it up.. good holding power but depending on stone can be a problem to drill,, might check the fireplace to see if there is another way to fasten it .. good luck!

What kind of stone? Is it Slab? Marble? sandstone? River rock? Morter joints? Old ? New? All of these things will affect the "best" fastener and how to apply them. If it is old with old morter, be VERY carefull using a hammer drill because it will loosen the morter!

For a general way of attactching, I'm going to assume older brick or block structure with a veneer of stone as this has been the most common type of construction from my experiance.
Drill through the veneer with a mason's bit without the hammer functioning, once you reach the structural part of the fireplace, use hammer function but don't push to hard, let the drill do the work.
I would use a quality wedge type anchor or epoxy set socket or stud depending on all I the verables mentioned above.
Good luck!

Yeah Photos would help determine the favorable route(s) If there are motar joints in the right locations, I like to use those. Usually much easier to drill and still strong enough to hold most concrete anchorings i.e. lead anchors, Red Heads etc.

If you build the frame so it overlaps the outside a bit and has some clearance inside the sides, say 1/2" or so you can make feet on screws. The screw heads will be hidden in the frame, then pass through the frame in threaded holes to the "feet."

Then all you need to do is slide the screen frame into the fireplace and tighten the screws. Done deal.

It's easy, fast, requires a minimum of precision measuring and forming, can adjust the screen's position and makes it removable for repair, etc.

Frosty

Can't say I'd recomend using either epoxy or zinc anchors in a fireplace or anywhere that gets very hot. Most any type of steel anchors would be fine though. Actualy Frosty's method is even better.