If you have to fly into Eureka, you will fly on either United Express or Alaska Airline's, Horizon Air. Our airport is small. (code ACV) If you have your own plane, you can fly into ACV or an airport closer to Eureka named Murray Field.
I would recommend you drive to Eureka. You don't want to miss the gorgeous coast line, tall Redwoods and interesting stops along the way. If you drive from the south, be sure and drive up Highway 1 if you can. It is a very scenic, twisty alternate route along Highway 101.
There has actually never been a 'working' railroad as long as I have lived in Humboldt county, but every year or so there are whispers of 'someone' starting the old wheels turning again..It would be great to have this kind of transportation between here and San Francisco. At this point,driving, walking or biking are your best options as flying can cost as much as a cross country flight. I am not holding my breath for train service to resume anytime soon.