Yes, you'd need a strand of yarn for each color section, so one for the right edge, one for the circle, one for the left edge.
When you change colors, hold the color you're dropping over to the left and bring the new color up from under it to twist the stitches and avoid holes.
Amy's video on Intarsia should help, too.
"Trust the pattern!"
Time flies like an arrow, but fruit flies like a banana.
Hop aboard while we follow the cloud-covered van of knitting harmony, man!! Woooo!! --Hedgehog
IngridKH on Ravelry