route from salt lake city to redwood national forest

I assume that you are asking about routes to Redwood National Park in CA, there is no Redwood Natl Forest. Years ago some of what is now Redwood NP was created from portions of the Six Rivers Natl Forest which is headquartered in Eureka CA. Both of the routes suggested by msmith1199 above are good, we usually end up on I-5 and cut over to US 101 by using CA 20 at Clear Lake. There are many CG's in the park and also some great places in the adjoining CA SP's that comingle with the NP. Stop at the Samoa Cookhouse just west of Eureka for a reasonably priced family style meal and take in some of the old looging history of the North Coast!