One of the reasons I wanted to write this blog is because Mammoth Mountain, bless their souls, is terrible at explaining how some things work. Maybe they don’t want to highlight certain aspects of their operation and instead focus on SHREDDING POW BRAH. But other stuff matters, so let’s talk about dealing with your car.
There is also the Mammoth bus/trolley/shuttle system which I won’t cover much in here beyond the parking shuttles.
Unless you’re coming from outer space, you’ll take the 395 to the 203 to get to Mammoth.

Mammoth has three lodges (aka places that have chair lifts, sell coffee, sell lift tickets, and have parking): Main, Canyon, and Eagle. Main is the biggest and is open when the others aren’t as it’s the highest in elevation. Two other quasi-lodges exist that are worth mentioning.
The Village. Open year round, there is a gondola that will take you to Canyon Lodge. There’s also coffee, places to eat, places to lose lots of cash on clothes, and you can buy lift tickets here. But if Canyon isn’t open I’d skip it. There is a bus every ~30 minutes that makes laps between the Village (across the street, near the parking lot) and the Main Lodge.
The Mill. At the base of chairs 2 & 10, there’s a parking lot and a small restaurant. Early and late season chairs 2 & 10 aren’t running, so this might not be the smartest idea at those time. No ticket sales, so you’ll need to have your pass on you as you’re just walking up to chair lifts here. There’s a decent parking lot if you show up early.
When the mountain is “fully open”, that means that all the lodges and all the runs are online and you can pick whatever you like. But figure that out in advance and if you don’t know shoot for Main. Drive your car as far up 203 (Meridian / Main St) as you can and try to park near one of these signs:

A constant stream of free busses run between the Main Lodge and the parking signs doing laps. You probably will only wait 5 minutes, but sometimes in severe weather or really busy weekends I’ve seen it take 15.
If you’re at Parking A, walk unless you’re really beat up or in ski boots. If you’re at B and have the legs (and again, aren’t in ski boots), go for a stroll. C or further down you’re dumb as a post if you walk. Make sure you grab the bus on the going-to-the-mountain side of the street.
Also, even if you want to walk remember that it’s probably windy/snowy/icy and that busses are flying around. It’s not the safest place to be on foot.

Bring all your crap with from your car that you’ll need for the day. You can always grab the bus back to your car but that wastes time unless you’re done for the day.
Remember what parking zone you’re in, what side of the street, and whether you’re before or after the post. All SUV’s and Subarus look the same when covered in snow.

At the lodges you can also pay $25 to park right up close. Although this is rather dumb for most people, I would recommend it for first time visitors especially those with kids or that just has a big group. It’s hard to know everything you’re going to want and it’s easy to forget stuff when you’re worried about your kids. Also consider that locker rentals are $5 per use. So if you open a locker up and close it again you’re halfway to the cost of having your car right there in front of the lodge building.
Hopefully this can help some folks navigate the rather dizzying web of lodges, quasi-lodges, gondolas, roadways, parking zones, and shuttle busses that Mammoth has to offer.