I actually tried using two very different types of paper. The one above is made with tracing paper: I just roughly brushed on varying shades of purple and let the paper dry. Then, I cut petal shapes from the paper, brushed Mod Podge onto the backs (one at a time), and smoothed them to a scrap of sturdy card stock. I added a second round of overlapping petals to the first level, ending up with five over five. This photo shows a second flower made using this method, sitting on top of the cut-up paper.
More photos of the two effects: