We hiked for about 1.75 miles til we got to the waterfall, and then headed back. I didn't see any trace of the mine itself, although I have seen it before. Just couldn't find it this time around.
It's not too difficult, although you do have to keep your balance often, since there are a lot of rocks to jump once you get to the creek.
To get to this hike, you'll drive to Chaney Trail (from Loma Alta Drive in Altadena). Follow the road til you get to the second gate (you'll probably see other cars parked here). Follow the trail about 1/2 a mile til there is a small dirt path on your left. Follow that trail down into the canyon and once you get to the creek, keep following the creek upstream. There are several times where you might lose the path, just keep going upstream.
Another route: If you drive too far, you'll go down the hill to a huge parking lot. This apparently goes to the same trail. However, I've never taken this route, so don't take my word for it. I found another blog that has a pretty good write up: http://www.hikespeak.com/trails/dawn-mine/ and it also talks about the details of getting to the mine.