I tried this with dd#2. Problem was I had an accidental unassisted birth. Then the placenta ended up down the toilet & then in a plastic bag & transported to the midwives. So by the time I got to try to placenta print it it turned into a total splodge. With dd# 3 I forgot, until after I'd had to thaw her placenta to make room in the freezer & had planted it out the back block.
In theory, if I was to remember again, what I would do is get a pad of appropriate sized watercolour painting paper. I think you need to drain it off a bit so it isn't this blob of a blood stain. Then I would gently stamp the different sheets of paper with it.
I found these instructions on the net. I would use watercolour paper as it is more absorbant & textured so I think it would get the patterns a lot better.http://www.birthdiaries.com/diary/48vbirth2.htm
There are some hysterical comments in the comments section of that web page about it. I dread to think what they would say about the prospect of eating a placenta