Go to Yosemite and prepare to show your paperwork. I have been checked as many as three times in a single day in Yosemite. I have been asked for permits in SEKI. I have not been asked in Dinkey or Ansel Adams but at times that is trail crew for me, and we are with the ranger who has a special permit for the group on official trail crew trips. And when it's not trail crew, the rangers recognize me from trail crew
I have been checked at trailheads. I have had the bear can checked for, multiple times, as well.
So to find out if you need a permit (you often don't if you are not targeting overused, overtrodden, overpopulated areas of the Sierra) you visit google and put in the name of the wilderness area. Yosemite allows you to reserve 128 days in advance. In SEKI you start reserving in March -- for dates all year -- so if wanting to go in September, go to the Sequoia/Kings Canyon page NOW and follow instructions.
If you want to backpack the Lost Coast trail, the considerations are different - permits are not so much a problem as transportation to the trailhead. If going anywhere in the wilderness of Los Padres National Forest (there are multiple wildernesses designated there) you need no permit at all. If you are going to Golden Trout, there are no quotas and no fees -- they just want to know you are going, essentially.
Inyo NF allows you to reserve online so if you want to start from a trailhead anywhere on the east side of the Sierra Nevada, check that page on recreation.gov to see about quotas (usually large) and lead times and other regulations.
Ansel Adams Wilderness has trailheads in Sierra National Forest, which are not typically so difficult to get as in the park system. I only reserve for holiday weekends or groups larger than 6. The roads to trailheads are more the concern there.
BLM properties that are backpack-able typically do not require permits. In some places what you are getting is essentially a camping permit -- you backpack in Point Reyes, for example, and you are paying for a spot in a designated walk in campground.
In other words -- there is no single answer. Look at the website for the place you want to go, and read about it. You will find that reservations are only really ever necessary in specific, heavily-used places like the parks. State parks, like Henry Coe, can have backpacking - but look at Big Basin and you realize that again, you're actually paying for camping. And Big Basin does not allow dispersed (camp anywhere) backpacking due to extremely heavy use. Henry Coe on the other hand is a great place to JUST GO because you reserve nothing -- you simply choose a zone and pay a fee, and while the hiking is strenuous and summer is LOUSY and HOT and sometimes waterless, it's good hiking in winter and spring. (You need good tick prevention measures, however.)
The real concern will be the different needs for food storage and cooking - visit the Ventana Wilderness and you will not only face a fire ban in summer, you won't be able to use a stove at all, because that place is such a tinder box. And water sources are a critical piece of research that must be done. Fortunately there is a forum with locals frequently updating trail conditions.
The Sierra Nevada is a piece of cake for backpackers, but is accompanied by loads of red tape most places. Exceptions like Jennie Lake Wilderness (no permits) and Saddlebag Lake loop (permits are free without quota, no fires ever, but a great fallback if you can't get the walk-in for a Tioga Pass/Yosemite trip) will likely see changes in the near future, to throttle back the HORDES of hikers flooding the trails. And the famous John Muir Trail is so impacted that they have had to seriously squeeze the quotas down, so 90% of the folks attempting to get permits will fail.
But, stick with us long time backpackers -- there are tons of comparatively unknown places to go just as gorgeous, and relatively untraveled.