Sorry it's taken so long to respond to this; I was out all day at Pagan Pride Day.
The answer: rather messily. You mix it up more or less the same as you would for body art, but a greater amount. Mix the dried henna powder with an acidic liquid - some people use tea, I prefer lemon juice diluted with a bit of water - to the approximate consistency of very wet, spoogy mud. Then you need to let it sit overnight (about 12-18 hours is the best window at room temperature). Wet your hair. This is important if you don't want to have massive tangles later, as the henna mud is pretty thick. Depending on how long the hair is, divide it up into sections. Put on gloves, apply liberally, wrap it in plastic wrap (I like Press-N-Seal best), and then wrap a towel around that. Holding in warmth will help the color release faster.
I usually leave it in for about three hours. After that, hop in the shower, and rinse, rinse, rinse. Go ahead and shampoo and condition as well, and just make sure you get all the mud out. It won't stain porcelain or synthetic fabrics, so most baths/showers/curtains should be fine.
At first, it will look very, very orange. It needs a couple of days to oxidize and darken. What color it turns out depends on the color you start with; for my naturally strawberry blonde (heavy on the strawberry) hair, it comes out a brilliant and very natural-looking shade of red. True blondes will be a lighter red, light brunettes will be auburn, and dark brown to black hair will pick up reddish highlights. It won't ever make hair lighter, but the red you get does not fade. Chemical reds start to go at about 4 weeks in, but henna is forever.
And literally forever, too; it actually seals off the hair shaft, which then resists taking any chemical colorants. The only way to get henna out (without destroying your hair with bleaching, which may not even work) is to let it grow out.
I shudder for the sadness of that alternate universe that has not been exposed to the awesomeness that is me.
Do not cheat yourself out of the first appearance of River Song. The creepy is worth it.
...I actually think I need to go back and watch it now, with the new perspective of knowing everything that she's been through leading up to that episode.