Karen: Many times picture mats are sold with a cardboard back. You could carefully glue a ridge around the in the inset of the frame and place in the cardboard backing. Lay very flat until totally dry.
You can try a very thin piece if MDF.
If you are hanging it on the wall and the back will not be seen, try using a piece of cardboard cut to fit with picture frame tabs. Depending on how expensive you want to go and if you can see the back, you can also use a thick sheet of card stock in the color that you like, add the picture frame tabs, good to go. They do make a picture frame tab tool. Hope this helps.
Hello. Most times the art pieces or canvas panels are fixed in with glazing clip points that might normally use for windows. They can be triangular or sort of M shaped. In addition sometimes tiny nails or staples are used If this can be tolerated by your frame without damaging it.
These glazing points can be purchased at art stores craft stores hardware stores or even Amazon.
Here’s a link that might be helpful
How to Use Glazing Points & Picture Frames : Picture Frame Crafts https://youtu.be/0Tq2MN0w7hk
I usually put a piece of cardboard behind the photo. If the backing shows around the photo, try adding some white or decorative paper first. You can glue the cardboard, as someone suggested, or put some tacks or small nails in the back of the frame to hold the cardboard in place.
This might help:https://www.youtube.com/watch?v=GkviR6IbsW8
What type of material is the frame made out of - metal, wood, plastic ?
How heavy is the 'picture' you want to display in the frame: - is it a photograph, is it a thicker art canvas, etc?
Several frames in variety of materials and sizes
A cardboard/poster board back is usually used. Picture frame push points hold everything in place.
I have used tape to hold backer onto the frame. They do make push point tools, but that is an extra expense - especially if you don't mount a lot of pictures. I just found this on Amazon for $10. Mechanical tools are $35, $65, and higher. I have always just used a wide flat-heat screwdriver and wiggled them into the frame.
You could add cardboard if the backer is missing. Tape in place.
I would add a piece of thin wood to the back of the frame with small nails.
Good idea,thanks everyone