Hi Connie,
As luck would have it I just finished a couple of those. We like to save of our suede scraps for this purpose and we also make most of our redi-made frames this way as well. Cut your mat about an 1/8 of an inch shy of the dimension of the back of the frame. Measure how wide the moulding is and cut a fall out just like you normally would, bevel and all. We use a thin layer of glue to hold the backing onto the back of the frame, but we also use those tiny little nails too.
Turn buttons are available for this purpose from United Manufacturing. Two on each side is usually sufficient. If you wish to build your own easel backs United has the hardware for that as well. We have an array of sizes of easel back templates for different sizes and frame shapes.
If you choose to build your own easel backs, double up the mat board for stregnth on the easel arm.
Fill yor excess area with scrap foam center board. That way your back will have support and will not just be supported by that small bevel on the mat cut.
Good Luck,
Lori