Of the multiple different ways of teaching there are a lot of similarities that are common to them all. Even if you are learning using electronic keyboards instead of a proper piano, the instruction you will receive will be virtually the same. The aim of the majority of beginners is to be able to play a little in many styles, they want to be able to play classical, jazz, pop etc and most want to have the skills to play by ear as well as read a little music too. They may also want to learn how to accompany singers and other instrumentalist.
As a beginner, to have such goals could sound somewhat ambitious but before you start your learning journey you will need to get clear what you want to get out of it. If you put your mind to it you will soon be accomplishing many of your goals.
A short while ago I had to write a review for a home study piano course called 'Piano For All', I loved the method they used for teaching. The fist thing they teach is how to recognize the notes on the keyboard.These same notes are then shown to you on the musical stave so you can go about familiarizing yourself with them.The next step is to show you how to play a simple melody which entails using all of the fingers, as a leaning aid. The melody is written out so you can see it and there is also a diagram of the piano keyboard to remind you where the notes in question are
That is only the first part of the first lesson. Next you are shown the three notes that make up a basic chord. To play the chord they give you a simple little rhythm to play. Next you are told to duplicate the first note of the chord with your left hand but an octave lower, this gives you a bass note. They give you a rhythm for the bass note and suddenly you find yourself playing a musical phrase that sounds good and isn't difficult to play at all.
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Once you have this feeling easy to play, which will be almost immediate, you will then be shown two or three more simple basic chords. With the handful of chords you now know you can put them to one of the rhythms you have been taught and playing the chords in a sequence you will find yourself playing recognizable songs. This is a wonderful way to learn the piano as it can make you feel secure and gives you an appetite for learning more. As you move on you are taught some different chords, different rhythms and tunes. For each exercise you will see the notes you are playing written in keyboard diagrams and traditional musical notation. You will realize that you are suddenly playing keyboards or piano in much less time than you imagined.
In my opinion this method of learning is one of the best as it encompasses playing many styles of music from classical to pop, rock, jazz and gospel. It also teaches you how to read music and play by ear and as such is very effective.