Spearmint will fill up the whole yard if you let it. It grows like crazy, and will choke just about everything else out.
The wall of mint. :)
I cut handful to dry (cutting at least 2/3 of the plant off). I stripped off lower leaves, then tied them together with twine. Also, I flattened the bundle out (like a "Japan fan") so that it dries more evenly.
You want to cut it right as it's budding. That's when the essential oils are at the peak. In general, I think that's true of any herb. On mint, if you wait till it flowers, the plant will lose some of the potency. Also, you don't want to wait too long; the tiny seeds are are to some degree toxic (though I'm not sure how many you'd have to eat to get sick).
Also most things I've read recommend cutting it early in the day before the sunlight beats down on it. The light will reduce some of the essential oils.
Hang it upside-down away from sunlight in a well ventilated room. The oils in the stem will flow down into the leaves, when drying.
It takes a few days to dry.