I started learning the piano a year ago but unfortunately back then I didn't have an excellent teacher; instead of working on reading notes which I'm really bad at, we focused on my playing skills I finished Hanon, and I was working on Beyer at the same time; I also learned a couple of other pieces.
But the thing is I memorized all of it, Even with Beyer I usually just memorized the lessons that I had for the next lesson and I played it from memory, I just looked at the sheet to know where I am and occasionally read the nuances.
So now I can play pieces like Chopin's Nocturne Op. 72 No. 1, and Mozart and Mendelssohn pieces and I also can read single lines of music, but I can't read both hands at the same time, not even on the really (really) easy sheets.
This month I changed my piano teacher and he is one of the best in my country; he is more than qualified to teach, He gave me some really easy sheets and told me to practice them and if I started memorizing just play random parts of the song of the sheet. I've been trying to do that but I haven't made much progress yet, so if you have any advice, like how you learned to read music sheets, or tips on getting better faster I would really appreciate it.
Also, if I'm not clear enough on this, when you want to play a relatively easy song, do you need to take time to read the notes and memorize them or can you simply play off the sheet? For me (when I was learning those couple pieces) it took a really long time to go through the sheet measure by measure, and playing really slow until I have the piece in my muscle memory, is that usual for learning a song or I'm doing it wrong?