I'd chuck the woolworks one and go with the first Phentex one. That woolworks one is written in about as complicated a manner as you could find. So. . .
You DO knit every row, and you're going to use 2 colors, we'll call them A and B. There is a very important note at the bottom of this, so read everything first!
Cast on the 66 sts with whichever color you choose.
Row 1. Knit 6 with A, 6 with B, 6 with A, 6 with B, etc., until you have knit across all 66 sts. This will give you the beginning of 11 squares: A B A B A B A B A B A.
Row 2. Do the exact same thing as row 1.
Keep doing these 2 rows until the first set of squares is as long as you want them to be, just making sure that it's an even number of rows.
Now, you're going to knit every row to look like this: B A B A B A B A B A B. Keep doing that for as many rows as you did the first set of squares (that is, if you want even looking squares:) ).
Now go back to the first set of squares. Etc. This will give you your checkerboard.
So here is the important note. Since you are changing colors all the time, you don't want loops hanging on the inside, where you leave off 1 color and pick up the other. This is called stranding, and you just cross the 2 yarns over each other every 3 sts. So half way in every set of 6 sts of 1 color, cross the second color over it in the back of your work. Also do this every 6 sts when changing colors so that you don't get gaps between your squares, horizontally (vertically you will have no problem with gaps). Go to "Videos", above, go to advanced technics, and scroll down to knitting with 2 colors at the same time, stranding method.
And this is why it has to be an even number of rows: You need to change yarn for the next set of squares (from BABABABABAB to ABABABABABA and visa versa) always on the same side (THE RIGHT SIDE) so you don't get the new color showing up as a half set of purl bumps on the right side of your work. Try it-- when you change colors, the side facing you will have a nice color change, but if you look at the other side, it will have that half-bump new color thing going on.