The best way to get a site in the campgrounds that don't have reservations is to show up when people are leaving. I've always been able to find a site this way, even on a Saturday. So just be there around 10am look for the people that are packing up. Then snag their site as they leave.
Campgrounds
- Porcupine Flat: Pretty but stays wet the latest of all the campgrounds. Rear section not suitable for large RVs.
- White Wolf: Flush toilets and running water but feels more like a Valley campground.
- Yosemite Creek: Long winding one lane road means isolation and few to no large RVs. Often not full even on weekends.
- Tamarack Flat: Another long winding road but closer to the Valley than Yosemite Creek. Lower altitude means warming temps.
- Bridalveil Creek: Only Glacier Point Road it is the only first-come, first-served campground that's not accessed via Tioga Road.
But I really want to stay in the Valley
You might be able to get a site at the campground reservations office in the Valley. But you will have to be in line very early in the morning and, if you do get a site, it'll probably be for only one night and you will have little to no choice of which site you get.
The other choice, Camp 4, is a walk-in campground located at the Upper Yosemite Falls trailhead. Be in line early to get a site.
What if I am coming up on a Friday night?
If you are coming up the east side (i.e. on highway 395), I suggest dispersed camping east of 395 north of the Mammoth Lakes exit. There are many dirt roads in the area and you'll have no problem finding a place to spend that night. Then you'll be in a good position on Saturday morning to get into Yosemite and find a site for the rest of your trip.