This particular cast-on is my bread and butter. Part of the stretchiness experiment is just to get me to branch out and try some other methods. It's a great one to teach to a first-time knitter, because it's almost the same as the knit stitch so you're killing two birds with one stone (although I don't know if I'd want to learn knitting from a bird killer. You should probably try to cut down on that).
The knitted cast on:
Start with a slip knot:
This is your first stitch.
I usually leave a good 6" tail on the non-working side of the knot for weaving in later.
It doesn't matter which way you put it on the needle.
Put the needle with the stitch on it in your left hand, and the other in your right hand. Keeping the yarn behind both needles, insert the needles in your right hand knitwise (from underneath, going upwards) into the loop, from the front to the back.
If 'front to back' doesn't make sense, just make sure the tip of the RH needle ends up behind the LH needle.
Take the working yarn in your right hand (it's still behind the needles, right?) and wrap it counter clock-wise around the LH needle, bringing it between the two needles:
Bring the tip of the RH needle down and back out the loop, catching the yarn you just wrapped around the RHN:
Creates a new loop on the RH needle.
Slip the new loop from the RH needle to the LH needle; LH needle goes from underneath upward through the loop on RH needle:
Now you have two stitches cast-on:
Repeat (excepting the slip-knot part, of course) until you have the amount of stitches you need.
Here's what it looks like on a ribbed swatch:
It's a bit messier than usual since I cast-on using a needle 3-sizes larger than the one I made the swatch with (to allow it to stretch farther). That is a drawback to this cast-on: it's not super stretchy, and the only way to compensate is to do it loosely. I don't trust myself to do it loosely with any kind of uniformity, so I just use needles 2-3 sizes larger what will be used for the body. I've reached at least one conclusion: I'm not going to be a hand model any time soon.