One of the hardest things to learn when beginning to play the piano is hand independence.   At first it seems complicated just getting your fingers on one hand to flow up and down the keys the way you want them to, without worrying about what your other hand is doing, but it does get better!  There are two methods of improving your hand co-ordination that you can try to see if they help.

Firstly, practice each hand separately.  Practice the notes on the right hand first of all.  Get the melody straight in your mind.  Learn how to place your fingers so that the notes are comfortable to play and don’t have awkward reaches.  Start off slowly, use a metronome to learn the timing of the piece of music, and slowly build it up to where it’s supposed to be.  Do the same with your left hand.  The harmony on the left hand will be more chord related than the melody.  As with the right hand, practice will help you remember which keys are involved with which chords and this will become easier for you to remember.  Use the metronome to help you build to the correct timing so that you are playing both right and left hands at the same tempo.  Once you are comfortable with both hands, bring them together.  You should try to put them together at least once per practice session so that you get an idea for how you’re progressing. 

The second method is to play both hands together but very slowly.  Ignore all timing until you’re comfortable with your ability to move your hands in different directions at the same time.  Acknowledge that this isn’t an easy skill, and that your progress in achieving this is a great step forward in your skill as a pianist.  The more times you practice, the more proficient you will get at this skill.  You’ll find that by practicing measure by measure you start to move your hands almost without thinking about it, and that’s when you’ll know that your training is paying off!

The worst thing you can do is to focus on the fact that you need your hands to do completely different things at the same time.  When you are relaxed and not thinking intensely about it, you’ll find the skill comes a lot easier.  If you start to play and you find that your left hand is all over the keys because you can’t look at both hands at once, concentrate on playing the melody.  If you are reading music, look at the music not your hands, with practice your fingers will know where they’re going without you watching them.  Trust in your ability to play the music.  As you relax and hear the melody, the harmony line on the music will grab your attention and you’ll find your left hand starting to play.  It might not be perfect at first, but that doesn’t matter.  The aim is to get both hands moving in different directions at the same time. 

As with patting your head and rubbing your stomach, it’s when you are least focused on what you’re trying to achieve that you’ll succeed in playing the piano with both hands.   Once you’ve mastered this skill, you’ll find that it becomes such second nature that you don’t think about it anymore, you just put your fingers on the keys, and play!