The sheet music containing the musical notation is by far the best way to learn new songs thoroughly. People who have trained in reading sheet music can play a new song instantly if they are given the sheet music. Learning to read the sheet is very important part of learning the piano, and here is how you can do it fast.
Reading the sheet music might take a long time. Playing from it will take longer. But all this if you do not know how to do it smart. Some people go to regular classes to learn piano, but sight-read poorly. Some learn all by themselves and yet, are good readers. The reason for this discrepancy is that sight-reading is not some mechanical, robotic process. If you treat it as a natural and easy process, you would not find any difficulty in learning to sight read.
The greatest thing that you can do first is learn to sight-read the notes of famous songs that you already know by heart. To begin with, learn to play the songs on the piano through some means. This way you will know the notes and the duration. Next, take up the sheet music for the song and go through it. Knowing the basics of notation and the clefs would be a mandatory, though.
This way, you will get a feel for the notes and the durations automatically. Furthermore, what happens when you do it this way is that the note-data that your eye sees directly gets transferred to your fingers! These days, even piano learning softwares help you out in learning to read sheet music through such interesting processes.