You will need:
An old shirt, preferably knit fabric
a circular template, I used a plate
something to write on fabric
crochet thread or maybe embroidery floss (mine was a little thick, so sewing it was a pain)
circular knitting needles
Turn your shirt inside out. Make sure the back of the shirt is facing you (or whatever part you want the knitting to cover).
Trace your circle. It might be good to make sure the placement is right. You could use other shapes too, but the math will be different.
Cut out your shape. Fold over the raw edge about 1/4 inch on each side. The knit stretched enough that the fold was really clean. Pin in place.
Knit a gauge swatch in stockinette. I used size 8 needles to make a loose fabric. Measure the stitches and rows/inch.
Measure the radius (distance from middle to edge) of your circle. This will tell you how many rows (rounds) to knit.
This and your gauge swatch will tell you how many stitches you need in your first round.
Subtract 2 times the height of one row of stitches from your diameter. Multiply this by 3.14 to get your next circumference. Use this to figure out how many stitches in your next round.
Continue this process until you get 0 for your diameter. Now you can figure out how many stitches to subtract each round. If your number is consistent, you can create your decreases at the same point on the circle and create sort of a pattern this way. I distributed mine randomly.
Using a whip stitch, sew the number of stitches you need for your first round around the circle. This was difficult because of the thickness of my thread so I advise using very fine crochet thread or using embroidery floss.
Turn right side out and knit once into each sewn stitch. Continue knitting following the pattern you created until you reach the middle. Draw the thread through each stitch and pull tightly. Weave in ends and wear.
I hope this made sense and also that I didn't over explain. Please comment with any comments or questions or feel free to email me. Thanks for reading!