I play piano quite well, but unfortunately I've only learnt by sight reading, and sheet music is expensive, and hard to come-by. I also have trouble learning via youtube tutorial videos, are there any exercises I can do to start learning by ear??? I wanna be able to hear a song, and know what notes are being played and hopefully learn the song within a month for a simple-ish song.

do develop the ear and note recognition you have to find songs and sing them with the name of the notes, requires sheet music though...
that really makes you progress in finding notes of songs.
if u want to find chords it gets a bit more complicated but not impossible...
if u want to find some classical music for free u can check imslp.org ( there are probably easy songs there if u know them, like Schubert's lieder (quite a few are not so hard to sing, there are over 900 lieder so you'll have to search ^^ )
another option is to take theory lessons in which the teacher plays something you have to write down - i dont know the english name for that- ( that develops the ear ( notes and rythm).

what piano pieces are u currently able to play btw?

sing them???

umm top 3 off my head

kuja (ff9 piano theme)
liberi fatali (ff8 piano theme)
nuvole bianche

e/ I mostly wanted to learn this for more modern music, like just be able to hear a song on the radio with piano in it, and play it.

This post was edited by turtol on Sep 30 2013 01:35pm

yes sing them with name of notes. last year in theory I really felt an improvement when the teacher gave us pain in the arse impossible songs that I had to manage singing for the exam
it will help with modern music, though improvements are not done in 1hour, it's a long-term progress, like piano actually.

alright, i'll give it a go =O thx for the tips!