Putting a new seat on a chair?

I am refurbishing a small wood chair. It is completely missing the seat. I can’t figure out how to upload a picture, but I’ll do my best to explain my question-

If you picture a photo fame without the back or matting, just the frame, you have where the seat part of the chair should be. It has 4 supports inside the "frame" to screw the new seat into. Should i cut it to fit into the frame so the "fame" part shows? Or should I cut the wood for the new seat to overlap the "frame", and go to the edge of the chair? We will be re-painting the chair before installing the new seat, and we have all the equipment to cut it and drill it (a buzz saw and drill). It is a sturdy chair, it has no other problems besides the missing seat (not wobbly or cracked anywhere).

I also know how to make the seat comfortable to sit in (foam and upholstery).

I think you’re supposed to cut it to the same size as the "frame" and sit it on top…the screws should still screw in to hold it in place. I bought my sister some chairs like that and had to re-upholster them. That is how they worked and it worked out fine. If you cut it to fit inside the frame and all you do is screw it in place, unless there’s some other support underneath the "cushion", I don’t think that it will have enough support to hold someone up. Good Luck!