There are a number of flower patterns available online. I thank Nezumi World for the ingenious idea of starting the petals on the outside end, and knitting the middle last. http://nezumiworld.blogspot.com/2009/06/world-wide-knitting-in-public-day.html
I make a similar five petal flower but start it with a puffy center.
Any yarn and any size needle will work. I used worsted weight wool and size 9 needles.
Kfb in each stitch (6 st)
K garter stitch for 4 rows.
K2 tog across.
Don't BO. Cut long tail.
Thread yarn. Run yarn through stitches and along all edges. Tighten into a ball. (This is similar to what you do at the top of a stocking hat.) Knot yarn, weave in ends and cut. (If you aren't going to felt the flower, you can leave the ends for ties.)
Holding button-like center right side up, pick up 3 st along the edge.
PKP in each st. (9 st)
Next row, and all wrong side rows until the last: Purl
On each K row, k2 tog each end until you have 3 st.
S1 P2 tog, PSSO, cut yarn and pull through.
Pick up three more stitches along the edge of your puffy center, and repeat 4 times.
As you weave in the yarn ends at the base of the petals, sew the bottoms of the petals together so that they overlap slightly.
I felted mine, so it came out like this:
Then appliqued it to a purse: