Head to the peninsula by ferry if coming from anywhere further north than Tacoma, Washington. There are several ferry stops around the Seattle area. You can drive your car onto the boat and catch a ride out to the peninsula. Once on the other side, drive to Highway 101.
Follow Highway 101 to Port Angeles, Washington. Follow the signs to the Hurricane Ridge portion of Olympic National Park. This area offers a scenic drive up to the scenic view areas. There is a visitors center at the top. You can also go for a walk on the ridge.
Exit the park the way you came in and head back to the evening ferry. If you have more time, keep going on Highway 101 and stop every chance you get.
Visit the southern portion of the park if you are coming from the south. Drive Highway 101 north to Olympic National Park. The first area you come to is Quinalt. It is where the park meets the Olympic National Forest preserve.
Follow signs to the park. This area of the Olympic National Park is much less mountainous. You can park your car and go for a short walk and enjoy the diverse Pacific rainforest.
Continue on Highway 101 if time permits. From Quinalt you are about 24 miles from the Pacific shore. Although the park sprawls out in the middle of the peninsula, much of the shore is part of Olympic National Park. When you are ready to go, turn around and go back on Highway 101 south.