Most clubs judge a player's ability by watching him or her during a game, and the criteria don't vary a lot from one club to another (in fact, if you search online for "pickleball skill level definitions," as I did," you'll see many documents listing the same things).
I looked at a number of the online documents and compared their lists of required skills for the levels from 1.0 to 5.0. I've posted my compilation of the most common criteria on a separate page (click here).
Some players don't like skill levels. Certainly, these levels can cause problems when, say, a husband and wife take their first pickleball lesson, hoping to play together, and a short time later, one of them has progressed to a 3.0 level, while the other is still a 2.0. And then there's the argument that the freedom to "play up" helps you increase your skills faster. That's true, but mixed-level play often only benefits the weaker player (not to say you can't have fun playing with anyone, no matter their level). If skill improvement is the goal, it's best for everyone if players are at the same level.
It's hard to assess our own skills, and quite often we think (or hope) we play better than we really do. Having an impartial judge point out the things you need to work on to achieve the next level is helpful for structuring your practice AND it also tells you what you're doing well. It's important to take stock of this, too, as you strive to become a better player.
Taking a skill-level assessment in stride reminds me of what happens when I get a good edit for my writing. I come away with lots of things to work on, at the same time that I know the rest of my work is okay, and I can build on that foundation.
So take a look at my composite of the skill level documents. Take an honest look and figure out what you need to work on to get to the next level.