Andrew, I have used a few different methods, but the one that worked best for me was to set my plate between some linoleum or wood corners the same thickness as the plate. That will keep your plate from moving. I have used plexiglass to put over the paper so that my pressure is even when I rub, and it will not cause the paper to break down during the process. That also holds the paper in place.
Another thing you can do is leave enough space at the top of the paper to staple to a surface that your plate secured to with the corners.
Believe me it is all experimental, and each artist has their own preferred way of hand pulling prints.
Ah, make the most of what we yet may spend, before we too into the dust descend.... Omar Khayyam
Stone Chief Studio