you get to the point where you want the inner color to start and you stop using the outer color and start using the inner, kind of like you had run out of yarn and needed to tie on a new piece (you know have three balls of yarn to work with. When you get to the other side, you tie on the outer color and knit with that to the edge and come back. When you reach the edge of the inner square, you stop using the outer color and reach down and use the inner color yarn you left there - a slight loop brings it up. Across the inner square, you reverse the process, picking up the outer color the next row down. When you finally reach the top of the inner square, you keep on knitting with your original ball of yarn, tying off the others.
Depending on exactly what stitches you are using at the transfer point, the carry up loops are more or less obvious, part of the design or irritating, etc.

This is called Intarsia or Picture Knitting.

When you change colors, make sure you have brought the yarn around the first color so that it doesn't leave a gap.

There is a simple diagram at the bottom of this page under Intarsia that shows you how to do it:
http://www.ethk…

good luck