Yes, you can do it on your own which will cost you the price of public transportation plus the $10 entrance fee to the park. But if you want to spend more and do a really nice hike with a Sierra Club guide, check out Tom Martell (muirwoodstour.com). For about $75, he'll pick you up in San Francisco in the morning and drive you over the bridge to Muir Woods - cost of the tour includes your entrance fee. He does really small group hikes inside the park - he won't take more than 6 people max. When I went with him, it was just me and 2 other people.
He takes you on a good off-the-beaten path hike that gets you away from the tour bus crowds that come in to just snap photos and stick to the walkways. As long as you don't have any mobility issues and you are wearing some semblance of decent footwear (sneakers, trail shoes), it's not a difficult hike at all and Tom provides plenty of time to stop along the way for photos, to talk about what you are seeing and also to sit down and have some snacks and beverages.
You'll spend several hours in the park and when the hike is over, he will drive you back but he stops in Sausalito so you can explore the town and then easily catch the ferry back to San Francisco on your own (great views of the city and bridge from the water and you end at the Ferry Building which is a great place to stop for another snack or a late lunch if you don't want to linger in Sausalito.