I think practically every musician should learn to play by ear. I know that there may be a few people here and there that just can’t learn that way but most can. It is completely natural to learn music by ear; in fact, it would be easy to make a case that it is more natural to learn with your ear than by reading music with your eyes. After all, music is an aural thing!
While there are some child prodigies that come out of the womb playing by ear, the rest of us have to work at it. I never was encouraged to learn that way and never really tried to learn until well after college. And what I found out was this: you learn to play by ear by practicing it. For example, you intentionally start working on hymns without a hymnal in front of you.
Today, the truth is that I cannot even find a hymnal in my house. I don’t know that is a good thing; it actually embarrasses me a bit but it shows you how much I rely on my ear. While my children are in traditional music lessons with other teachers, when I am working with them, I teach by ear. If I am working with Kelsey on violin for example, I play a line on the piano and ask her to imitate it until she gets it right. It is not as tedious as it sounds; it takes about ten minutes to teach her a song that way.
For pianists, there are really only a few steps to playing by ear.
1) Learning to pick out a melody line only
2) Adding the basic harmony (initially as block chords in the left hand)
3) Texture (making it all sound good)
I want to cover these just a bit. I won’t go into too much detail because I have a course that does that. But this might help you.
First, picking out a melody line is something that practically any pianist can do. For that matter, any child can go pick out a song on the piano if she wants to. The key is to learn to do it accurately and that is just a matter of practice.
You can go about the process of learning melodies either by trying to learn interval identification and other theory-based things or by ignoring the theory and just practicing with songs you know. I see value in the first way but I strongly suggest the second. Just practice playing melodies by ear and over time, you will get good at it.
Adding the basic harmony is a bit more complicated but within the reach of anyone that wants to make the effort. The chords that you find in songs in major keys fall into a few groups:
1) I, IV and V chords (80-100% of typical hymns)
2) Secondary dominants (0-10% of typical hymns)
3) Minor ii, iii and vi chords (0-10% of typical hymns)
4) Other special chords of various types (0-3% of typical hymns)
I suggest you just ignore the last group for a while. That means you need to understand major and minor chords and how secondary dominants work. Secondary dominants take a bit of effort but they are necessary because the majority of hymns have one or two sprinkled in them.
And that leads us to texture. Texture is simply playing the song using various technical patterns and ideas. Arpeggios is an example of texture. Arpeggios are broken chords and can be played in short or long patterns in either hand. One of my favorite textures is left hand arpeggios of medium length.
You can get a lot of mileage out of just a few textural ideas that you can do well. Some professional pianists will have a huge palette of texture under their belt, but if you are just starting out, I would focus on only a few. For many traditional pianists, a texture you will want to learn is the common congregational style we refer to as stride.
That is about it. Playing by ear is not hard and almost anyone can learn it with some effort. If you do, your versatility as a church pianist will grow tremendously.