One thing you will not learn here is how to play the piano. If you want to be a pianist you need to find a teacher and get started there. If you are interested in learning enough about the keyboard to make it a useful musical tool then let's get started.
If the written note has a in front of it, play the note immediately to the right on the keyboard. If the written note has a in front of it, play the note immediately to the left on the keyboard. For example:
Try to touch the piano keys lightly and gently. If your fingers are rigid, stiff, with the anxiety of trying to get the right notes at the right time, it will be much more difficult to get it right. A relaxed hand is much easier to get the the right place at the right time.
Play something you like and that you are familiar with. In time, you will be able to look at any sheet of music and play something close to what is written, but there is no sense adding the burden of playing unfamiliar music on top of learning to press the right key. When we learned to type, we learned by typing familiar words. We didn't learn to type obscure chemical names or technical jargon. The same applies to the piano. When starting out, play what is fun for you. Anything you play will develop your skill.
If you are practicing to play by ear, play what you are familiar with: advertising jingles, TV theme music, popular folk songs, etc.
For improving Fluidity:
Do you play by ear? I recommend you try it. I found that my fluidity went up greatly when I started playing by ear. Or in other words, without any music, sit down and play the melody to some songs that are very familiar to you. Add some harmony as appropriate. This should be music that you have not previously played from a printed page.
Since I started learning to play by ear, the music I play from a printed sheet sounds better. My fingers just seem to anticipate where the next note is going to be, even if my eyes haven't quite caught up. You don't have to become an expert at playing by ear, but if you practice until you can do it a little bit, it will greatly improve your sight reading capabilities!
For Improving Memory:
Another idea that has more to do with biology than anything else, is to play the piece you are learning immediately before going to bed. It should be the last thing you do before laying your head on the pillow. During the day, our brain stores many things in short term memory. These memories are transferred to long term memory during sleep. If you are doing anything after your practice, the memories of your practice session will tend to get overwritten by the events you do later in the day. Playing the song one time just before bed, will bring these memories to the foreground. They will be transferred to long term memory more efficiently.
Keeping the Rhythm
The trick is to play what you play in the proper rhythm, even if you only play a portion of the song. In other words, practice keeping the rhythm going at the expense of everything else. Don't play the cords, or play one or two notes in the cord rather than the whole thing. Before long, you will be able to get more and more notes included in the cords, or you will learn which notes are optional. In most cases nobody but you will realize that there is a note missing.
Where to Put your fingers
The orthodox technique, for example if you are going up the scale with the right hand, would be to play the first three notes starting with your thumb, and then after playing the note under your middle finger to play the next note with your thumb again. (The thumb crosses under.) Going back down the scale, starting with the pinky on your right hand, you would play five notes, and then your middle finger would cross over the top of the thumb to play the next lower note.
Playing with the left hand is a mirror image of what the right hand does.
For regular music:
The same sort of arrangement applies, but it is also common to just pick up your hands and move them so that they span the next sequence of notes you are expecting to play.
Playing with Both Hands
(Nearly always) play with both hands, don't try to separate them.
Don't worry about skipping a note here or there in the harmony. If you don't get there in time, just go on to the next one, or make up a harmony! Few listeners will be able to tell. After a while your left hand will develop a feel for where the notes might be expected to be. After a while, your right hand will be able to pick out the melody essentially by ear without having to pay so much attention to the notes on the page, thus allowing you to pay more attention to the left hands harmonies. These two trends will combine together to make playing easier and easier. Doing a little bit of playing by ear, and a little bit of sight reading new music, will help to strengthen these trends.
Children and the Piano
So often, a parent will say, "Don't touch the piano", or "Quit making such awful noise on the piano", then the parent wonders why the children don't want to play the piano when formal lessons start. Children learn best by doing. Let them goof with the keys while you play. (It's less intrusive if you put them on the right side of you!) Or let them make horrible sounds by themselves, and if they accidentally play something that sounds good, be sure to acknowledge it, so it will be more likely to occur in the future. My son by the age of 8 was playing well both by reading music, and by ear, without ever having had a lesson. He just tinkered around. Not saying that there aren't some pretty unmusical things coming out of the piano, (even now), but overall the joy of listening to him play compensates for any bit of patience that was required.
Finding the Notes
To make it easier remember that the spaces in the treble clef spell FACE. To remember the lines use this Every Good Boy Does Fine.
On the bass clef spaces remember All Cows Eat Grass and for the lines Good Boys Do Fine Always. Start on the bottom line and bottom space for both clefs.
The library is a great place to find music. Especially if you are learning to sight read. You can check out a book, play the songs in it a few times, and then go on to another book. This way, you always have a fresh challenge and don't get bored with the same old stuff.
Another fun book to play from is called a fake book. They typically come with just the melodies of the songs, and perhaps recommendations for what cords sound good with a particular part of the melody. You make up your own accompaniment as you feel best. To the uninitiated, it sounds like full blown sheet music, but the pianist knows what's really going on.
Playing by Ear
The grand mystery to playing by ear is deciding which note to start out on. If you choose that note properly, the rest of the music is greatly simplified. It also helps if you play the music in the key of C (no sharps or flats). To choose the first note, hum the last note in the song as a C. Then hum the first note in the song, and match it to the piano. This is simplified, because the starting note will typically be one of the notes in the base cord of the last note. (see drawing below)
The cords illustrated below, on the bottom staff, are the most typical cords in the key of C, which is the simplest key to play in. The notes on the top staff are typical of what notes you might be playing at the same time as playing the cord.
I usually go about it the other way around. If I'm playing a C note in the melody, I will typically form a C cord with the left. If I'm playing a D with the right hand, I'll typically form a G cord with the left. There's no hard and fast rules, play what sounds good. (The small grids above the staff are for guitarists.)
Organs and Synthesizers
They're all played about the same way. On the piano, folks will often use the sustain pedal so that the note can be played, and then your fingers immediately leave the note and go onto another note. On the organ, you will need to keep your fingers on the key for as long as you want it to make a sound. Synthesizers may allow you to set this behaviour.
A Parting Word
And finally, relax. It's so easy with quick moving songs to let the fingers get all tensed up with the challenge of being on the right key at the right time.
Check out this site for instruction - How to Play Piano http://pianoplayerworld.com Your free resource and guide to learning the piano.