Previous answer is wrong (as in, not even close).
Here's the data for Half Dome. All times are PDT.
July 10, 2009:
8:22 PM sun sets
10:16 PM moon rises
July 11, 2009:
5:46 AM sun rises
9:48 AM moon sets
The moon is waning gibbous and about 86% illuminated that night -- a bright moon, though not quite as bright as full. It will be highest in the sky that night at 3:58 AM on the morning of July 11 -- due south at an altitude of 44 degrees.
Although I didn't use it here, the web site mentioned in the other answer is a good one:
http://aa.usno.navy.mil/data/docs/RS_OneYear.php
You can key in the coordinates for Half Dome directly, or you can enter the relatively nearby town of Bridgeport, CA. Remember that the information from this site is in standard time, so you have to add an hour to get daylight time.
I'm not sure this is really all that great a night; two or three nights earlier would be better for the following reasons:
1) Note that the moon rises nearly two hours after the sun sets. That means that it will get very dark before the moon rises.
2) What's your climbing schedule? As long as you are climbing up the Mist or Muir Trail, your eastern horizon will be terrible, so the moon won't even be visible until it's far up in the sky.
3) After you get over Nevada Fall into Little Yosemite Valley, things will improve; but Little Yosemite is a canyon, which means that you still won't have a good horizon.
In short, you will eventually benefit from the moonlight, but you'll have a substantial period before you even see the moon.
July 10 is a Friday, so you might be unable to go earlier. Don't even think about going unless you have ample flashlights and spares (batteries, bulb, extra flashlights, whatever you need).
