The first year or two of piano lessons is usually focused on learning the notes and becoming familiar enough with them to be able to read piano music. Once a student can read the music without needing to count the keys of the piano or ask for assistance with a note, they can take on more advanced piano music.
Most people learning how to play the piano rely on a series of learning books that become more difficult with each volume. The student is only allowed to progress to the next book when he or she can play every song in the current book without problems. Once this has been accomplished, the student begins the new, more difficult volume.
Some students make use of a metronome to help them keep time while playing. Piano music is partially dependent on keeping the time between each note consistent with the sheet music. The metronome can be set to keep time at the speed that the song requires.
Learning to play the piano is not something that can be done in a matter of weeks or months. It's a process that can take years of regular practice and dedication. Because there are endless books of sheet music, a student can make the study of this instrument a lifelong pursuit. Play the Piano and have fun!