If you have never knit stripes, or have never been satisfied with how you have been knitting them, you might find these basic tips helpful. (By the way, this isn't a tutorial on the "Jogless Jog", which is a way of eliminating the imperfect way stripes meet at the end of the round. Maybe another time!)
When switching colors, first make sure that the last stitch knit in that color (2 rounds ago in this case) is not too loose or too tight.
Now bring the old color (blue) over to the left, keeping it above the new color (white). When you knit the first stitch with the new color, the old color will be trapped between the working yarn and the knitting.
If you're an English style knitter (you hold the working yarn in your right hand):
When you knit the first stitch of the round, bring the yarn over your left index finger (this creates a little slack in the yarn to prevent puckering).
If you're a Continental style knitter (you hold the working yarn in your left hand):
When you knit the first stitch of the round, bring the yarn over your right index finger.
Remove your finger for the next stitch...
If you are using slippery yarn, like this silk alpaca blend, knit the next two stitches normally, but on the third stitch give a gentle extra tug so that the first stitch of the round won't be loose.
Here's what carrying the yarns up the back looks like:
And here's what it looks like in the front:
Notice how the stripes don't exactly meet at the end of the round. Don't worry, that's normal. It's because knitting in the round is actually knitting a spiral. So, the end of a round is one row higher than the beginning of the same round! When you block the knitting, sometimes you can kind of tug the stripes into alignment. (To learn about knitting stripes in the round without a visible seam, try searching the "Jogless Jog" technique!)