Basically, the original dog stake is a helix with a triangular handle, intended to tie up a dog on turf. About one foot long.
Screw it into the grass and hook a leash to the swiveling ring. The dog is unlikely to get the leash tangled up or wrapped on the stake.
Kiters liked to use them to tether single line kites.
At some point, someone put the lines from a stunt kite through the gap in the triangle and flew the kite facing the wind. Quad-liners soon followed.
The downside is that the inside of that sharp bend can be a bit rough, and that makes for fast line wear. Also, when you get several wraps, it gets hard for the lines to slide past each other.
The next phase was polished rings attached to stakes, and then pulleys, and then separate pulleys for each line.
John Barresi now has a custom-made 4-pulley "dog stake" (it's never seen a dog, and isn't likely to) that is a wonder.
If you want to try it, you will need a fairly long line set (100' or more; remember you are flying on less than half the line-length) and a stake and some kind of very smooth large ring or carabiner. Put the lines from your stunt kite or quad through the ring and set up the kite.
You will probably want to switch hands so that your normal flying skills will still work. Be careful to stand just a tiny bit farther from the stake than the kite, or you are liable to hit yourself with the kite. Mark a line and don't step over it.
If you are a flyer who likes to do a lot of moving up and down wind to increase and decrease wind pressure on the kite, you may find you don't like dog-staking all that much.
edit: heh, Watty was posting while I was editing.