If I like both sides, I might cut the page in half or in diagonals and glue the pieces to a solid color sheet, so I can enjoy seeing each side. I don't have anything uploaded right now, so I can't show you an example right now.
I am a lover of double sided paper. If one side is plain then I use that as a matting for my photo then I use the pattern under this. If both sides are pattern and I like I will use different sizes and layer.
The two sides are usually color coordinated with compatible designs. You can fold a corner down over the side you want on top (adhere it down or tack it with a brad or eyelet or something else) or cut or tear a hole or "V" shape in it and then fold the edges of the opening back and insert a photo or whatever underneath the resulting opening. You can do this with an entire sheet or just a piece of it. I've seen some really nice LO's done like this.