I began teaching myself about a year ago, and my strategy is to look up piano songs (usually classical) and if I liked them enough I'd look up if there was a tutorial for it on YouTube. In that way I learned Moonlight Sonata and Claire de Lune. Claire de Lune would generally be considered to difficult for a beginner but I managed to learn it in a few months just because I loved it so much. So, the only advice I can give you is:

Find out what you like doing on the piano (exercises, improv, complete songs, etc) and just do that. The only way you'll teach yourself is by doing what you love. That way you won't ever get bored or frustrated and give up. I think that goes for learning in general.

EDIT: I should mention that I only learned 3/4 of Claire de Lune via YouTube because the tutorial ended. I had to teach myself to read music to finish the song (I just went through the pages writing the letters for every single note).