1: Research. The web has an endless amount of websites which are there to aid you. Many include free lessons and posts answering your questions. It also helps to begin with a song you are familiar with and enjoy.
2: Positioning. Make sure you are seated correctly with your bench at the right height and distance from the piano, elbows should be at a 90 degree angle. No slouching! This will create back pain and fatigue, shortening your playing time, so keep a straight back! Also make sure your wrists are level with the piano, not too high or leaning down onto it, don't be lazy! You should also be playing with the tips of your fingers, not the pads. Therefore, it is very hard to play properly without short nails, so you ladies may need to trim a little!
3: Practice. You should be practicing daily for a half an hour at least if you wish to learn quickly. This includes learning the notes and chords, proper finger technique, accurate playing tempo, and many more details. Practice really does make perfect. When you practice, aim for quality, if your practice is sloppy then that is how your piece will sound. This will result in bad playing habits, which you will regret later. It is also a good idea to practice a seperate aspect at a time to improve them. If your left hand is slower than your right, play only the left hand of that peice till you perfect it.
4: Build finger strength. By practicing your scales, and increasing the speed as you improve, this will help to strengthen your fingers allowing for more speed and acuracy in the songs you play.
5: Allow frustration. This is extremely normal in learning an instrument. The three measures you've been trying to learn and memorize for a week will begin to sound clean and precise.
6: Play along. If you play along with the song you are trying to learn, this can you to learn the proper speed and sound of the piece. It is also simple to rewind and repeat small pieces over that need practice.
7: Frequent practice. Instead of practicing for long sessions only once in a while, try to make it more frequent and short. This way, your brain will memorize patterns and chords much faster.
8: Watch a friend. If you know someone who has experience in piano playing, try to meet every week to watch and learn how they play.
9: Change it up. Make sure you're not playing the same 3 songs constantly, in turn practicing no new playing techniques. Also try switching up the genre of pieces, playing different rhythms and tempos to get attuned to all types of music.