Ok, hopefully this will not be as confusing as I think it might be...I am going to try to explain it well, but we'll see what happens, hahaha.
I'm using two different sized needles because the different colors make it a little more clear what I'm doing. Normally you would use two of the same size. And this is going to be a little awkward until you get more stitches on the needles. You start out with only 5, and that's a little weird to work with, but it gets easier as you increase.
Ok, to start the Pinwheel Blanket, it says to cast on 5 stitches. You know how to do that.
Now if you had an even number of stitches, I would say to move half of them to the other needle, but since we have 5, we'll move just 2 over to the second needle. You just do that by putting your second needle into a stitch as if you were going to purl it (back to front) and slipping it onto the other needle (rather than actually purling). Just moving. This is called "slipping a stitch purlwise." Do that with two stitches.
So now hold the two needles so that the cast on edge is toward the inside. I've numbered the stitches (the first one you cast on is 1, and the last one is 5 in these pictures) to make it easier to keep track of them. Since you want to knit #1 first and it is on the wrong side of your needle, you want to slide the stitches to the opposite end of the needles. Just pull the needles up and slide the stitches down.
So it looks like this:
Now turn your work around so your needles are pointing up. Now you are ready to knit stitch #1.
You want to use the SAME needle, in my pictures it's the blue one. So get the other end of your blue needle and use that to knit the first stitch.
Knit all three stitches from the blue needle onto the other blue needle.
Now you need to get to stitch 4, but it is on the wrong end again. So you slide the stitches to the other end again. (You are basically going to be sliding back and forth every time you switch needles.)
So you get the stitches to the other end and then turn your work around, and you are ready to knit stitch #4, with the other end of the pink needle.
I often will leave the stitches you are not working on (the ones on the opposite needle) on the cable and just leave the needles themselves dangling. This keeps them out of the way and makes it easier to remember which needles you are working with. You don't have to do this, but I find it easier.
When you knit both stitches from the pink needle, you are ready to go back to blue. Slide again and this is what you have at this point.
I'm going to stop the instructions here, just to give you a chance to digest all this and practice if you want, before going on to the next step. It's not as confusing as it seems, but it might help to try it and see for yourself! Let me know if this does not make any sense!