There are about 25 sport routes (give or take). The Elwha has some awesome climbs and many sketchy climbs too, with loose/crumbling rock. The routes worth climbing, however, will have lots of chalk markings from other climbers, so its perhaps best to stick to those.
The first routes you'll encounter (Earth and Sky, One Shot Deal) can be top roped by hiking up the steep trail to the left of the crag and hugging a thin ledge (to the left side of Earth and Sky), which will put you at the chain anchor of One Shot Deal.
Also, even when its raining you can find a few dry routes to climb.