When you start learning a new piece, take in to account the time signature and key signature. Count out that beat and take care of which notes you should sharpen or flatten. Your first step is to try all the notes at a very slow pace, and your goal is for accuracy, not anything else. Continue playing slowly until you can feel the melody develop, and increase the speed. Make sure you count, so that you can play in time. After a while get a pencil out and circle the places where you make mistakes, and practise those parts only. After that, play the whole thing and repeat the process of eliminating those mistakes. Once you have gotten rid of those mistakes begin playing at normal speed.
Learning piano is not easy, and patience is the virtue for it. If you want specific help on some parts, feel free to upload a video and I'll help you out.
