Everything depends on your level of dedication. I think I would go so far as to say there is very little that can't be self taught in the world of music, after all there are only 13 different notes in an octave and the rest is just repeated at higher or lower registers. The only thing a teacher will do for you is to hone your performance skills and technique, other than that, you are doing all the work even with a teacher. For me, I find it very hard to sit down and just read dry theory books, I much prefer to have someone in front of me to explain things and for me to be able to ask questions, but as someone said earlier, You Tube has a huge amount of material for people to watch and learn from. If you have a good ear and are really dedicated to your instrument then the sky really is the limit.
As a child I always wanted to be a concert pianist, sadly we were not in a position to pay for the schooling that would have taken, but also I quickly learned that most concert pianists practice for a minimum of 5 or 6 hours a day, it really is a full time job and as much as I love my piano, 5 or 6 hours a day was way more than I could put in. I mention it only to give you an idea of the level of practice it takes to reach those heights. I'm sure your not wanting to become the next concert hall maestro either, at least not in the next few years, but you should try to put in at least an hour every day, even if you don't really feel like it some days, and you will very soon be able to play almost anything you look at. Once you know that basics, reading music is not difficult and even the most challenging works can be learned bar by bar if you put in enough practice.
The idea behind practice, practice, practice, is that eventually your fingers know what they're doing without you having to think about it too much, it's muscle memory. Do something enough times, and eventually it becomes sort of automatic. That's when you can start to concentrate more on the quality of sound, rather than just the reproduction of the notes. By the time a performer comes to play for an audience, they've probably played the piece thousands of times over so make sure you choose pieces you love :lol: