To get from San Francisco to Muir Woods without a car, you'll need three things: some time, some confidence, and ten dollars and fifty cents. Your first $2.50 will go towards your bus ride. Your next $4 will pay for your ferry ride. Your remaining $3.75 buys your seat on the shuttle into the park. That's all it costs to get you from the mainland to Marin! However please note that the government charges you $15 to enter the park. I don't make the rules. Anyways, with your wallet full of two fives and two quarters, you're ready to embark on your journey, which you can expect to take about 2 hours one way. How long you stay in the woods is up to you. Lastly, you just got to believe you can do it. Transit is your tool and it's your friend. This is going to be an adventure, and you're gonna love it.
The ferry building is a hot destination in San Francisco. That means there are a lot of transit options to get there. For me, it was the 1. But the 14. 172, and 5 all take you near there, as well as any BART line (disembark at Embarcadero), and the light rails F, K, and N. To figure out the best bus/train route to the ferry building, I recommend downloading the best transit app out there, the aptly named Transit.