Where does oil come from? Deep beneath the ground. When it bubbles up to the surface, usually someone declares it an oil field, pumps are set up, and unless you work there, you won't see this in nature.
The LaBrea tar pits are a terrible oil field (the quality of the tar/oil is not suitable for refining) but an amazing archaeological site. For the past 40,000 years or so, animals and other things have gotten stuck in the tar and preserved. For the past hundred years, we've been slowly digging them out. The museum has exhibits about those animals and the history of the tar pits (how indigenous people and others used the tar). I agree with other reviewers that the museum is not the best thing about the park - you'll have to decide if you want to see the 'preserved tar pit' and museum, or just see the amazing park.
There is a parking lot (pay to park).
Stay mostly on the paths and look out for little cones - those mark current asphalt "oozes", and you (or your kids) can lose a shoe to the sticky tar. So stay away from the cones, and be careful where you step. You can walk on the grass, even bring a picnic, but be aware that this is an actual active tar pit. Don't wear your best shoes, and be aware you might get a stain that will never come out.
There's a large tar lake at one end of the park where you can see and smell the tar in all its glory, and see methane bubbles rising. The smell is not overwhelming, it's interesting. There are several smaller pits, and a tent where you can watch volunteers, scientists, and graduate students slowly excavating one of the pits. I found that fascinating, personally (but I'm a scientist).
The park also has statues of some of the species recovered from the pits...nice photo spots. Guess how large a "giant ground sloth" is before you find the answer. And why do you think there's a picture of a camel there? Answers to these and other questions at the park (and in the museum). When we were there, there was also a (temporary) walk-in art exhibit that was interesting.
Whether you're into science or not, this is a must-see. You almost certainly have never seen anything like this, and probably never will. It's amazing. If you're into science, spend the bucks and also visit the museum.
About the museum, there are the cutest stuffed animals there. Probably not the most accurate representations, but adorable.