The levels categorise the exercises listed here into progression similar to the classical or academic dressage training. It's a guideline in how natural dressage can be achieved, but I would not cling to it strictly. There are too many variables (individual horses and humans, age, experience, environment) involved that might make a whole different approach necessary.
I see the levels as a very good listing of exercises and a good place to start and to come back for review. You can see the way they are organised in this post by Miriam
Still, for me the best way to start is to experiment. What does my horse know already? Where do I want to go from there? What kind of "exercise" can help me with that? No two horses will be the same in the way they learn.
There are certain exercises that are based on each other of course, like for example Jambette and Spanish walk. But there may also be horses who do Spanish walk just by themselves, so you just need to work on a way to cue that.
Basically all the Haute Ecole movements are inherent in horses, so it all boils down to the simple question of communication - a common language and an agreement of how to interact.
The rest then is just what it's name says: "exercise" (for body and mind).
You might also want to check out this thread: Different ways of starting to interact with your horse