Pull the new yarn through your stitch.
Yarn over with the new color, and pull through the two loops (one will be the original color, the other will be the new color). Your final stitch will be the original color!
...and your first sc of the new row will be your new color!
When you know you're good to go, snip off the original color leaving a tail to sew/weave/hide the end. You'll have to do this with the tail of the original color as well as the beginning tail of your new color so when you begin with your new color, make sure you leave a long enough tail! I usually give myself 6 inches or so with these tails--whatever is long enough for you to put a needle on the end and poke through a couple times. It's always better to have more than not enough.