You'll need to plan ahead and reserve a parking spot if you're going to drive out there. There's not a lot of parking so try to reserve it way in advance if you can.
Parking along side the road is no longer allowed. The roads are lined with no parking signs.
When you buy tickets to enter into the woods, ask when the next tour is. If the times are right, try to get the family on a tour so that you can really learn about the trees and the environment. If getting onto a tour isn't an option, try to attend one of the 15 minute talks in the Founders Grove. They really give you a lot of interesting information about the forest in that short period of time.
As you walk around the trees, look for banana slugs on the forest floor. You won't see a lot of birds. But the stream flowing through the woods might have fish or crayfish.
The main draw of the park/monument is the coastal redwood trees. These trees are tall. They're wide, but not as wide as the giant sequoias in the Mariposa Grove. They are definitely amazing to see.
Walks and Hikes
The main walk through the forest is pretty easy. If you're looking to get away from the crowds a bit, the signs will point you towards longer hikes through the woods.
Be sure to read whatever signs they have posted around the "boardwalk." The facts on the signs are quite interesting.