Negotiating Olympic National Park is really quite easy because there's one big loop road that circles most of the park, with spurs that run to specific destinations and attractions.
U.S. 101 wraps the park. From Olympia, you can either head north on the highway and cruise along the eastern boundary of the park, or go west towards Aberdeen and then veer north to run along the western edge of the park.
By taking the western approach, you'll pass Lake Quinault Lodge, Kalaloch Lodge, the various beaches (including popular Ruby Beach) accessed from the highway, turnoffs towards the Queets River Valley, the Hoh Rain Forest, the Mora Campground and Rialto Beach.
From Forks the road swings back east, leading to the turnoff for Sol Duc Hot Springs, Lake Crescent Lodge, the Elwha area, and on to Port Angeles, where you'll find the park headquarters, a nice selection of hotels, motels, and B&Bs, and the turnoff for Hurricane Ridge.
To reach the Ozette area with its lake and foot paths to the coast, just north of forks turn onto Washington 113 at Sappho, continue to Clallam Bay, and then a few miles west look for the Hoko-Ozette Road on your left. It runs all the way to the Ozette Campground along Ozette Lake, and the trailhead of the Sand Point and Cape Alva trails.
You can find some great maps at this Park Service page.