Hi, Lee and JJ! :waving:
This is one of those things that looks like rocket science when you're first doing it and then like kindergarden playtime once you figure it out. But for right now, it IS rocket science so let's see if we can get you to the kindergarden stage.
Think of your different colors as actors on a stage. They each appear on cue and then leave the stage when they've said their lines.
So, with that in mind, you'll cast on with Actor A (Color A) and he'll recite his lines for however many rows the pattern calls for.
Off stage Actor A goes and since his part is kind of long, we're not going to have him hover in the wings, we're going to cut him off completely. So snip that color yarn leaving a tail about 4 inches or so.
Then it's time for Actor B to strut onto the stage and say his lines. To keep him anchored, what I do when I'm changing colors is take the next color, in this case Actor B, and tie him in a single knot around the Color A tail. Then I can slide the knot all the way up the tail of color A and put it in position to begin knitting the Actor B rows. When I'm finished the piece I can pick apart the knots and weave in the ends (or even leave the little knots in place if you want to and weave in the ends.)
I hope this helps you get to the point where you're enjoying playing with the pattern and yarn and needles!