Muir Woods is an astonishing National Park, famous for it's 240 acres of old growth redwood trees, located 12 miles north of San Francisco. Every weekend, until September 27th, the Muir Woods Shuttle takes visitors from Marin City to Muir Woods and back. This is this only public transportation option to get to Muir Woods, which is well worth a visit.
There's a $5 entrance for Muir Woods.
The Muir Woods Shuttle leaves from Marin City and is operated by Golden Gate Transit. It's the 66 route, and the schedule and map are available here: http://goldengate.org/news/items/Rt66pr.php\
To get up to Marin City, you'd need to take 70, 80, or 81 weekend bus from San Francisco. Here's some information schedule: http://goldengatetransit.org/schedules/pages/Bus-Schedules.php
Redwood trees can grow to over 380 feet, and the oldest tree in Muir Woods is over 1,200 years old
More information is available at the Muir Woods webpage: