Well Hammondman and 4HisGlory pretty much answered your question and gave great advice. I can read music (sightread) and play by ear. When I'm learning a song from ear by listening to a choir or a recording, I pretty much focus on the instrument that I'll be playing like the keyboard or piano, sometimes the organ. You just have to drown out the other sounds and focus. After doing that you can learn the melody, so that can help you get the basic chords and from there you can add the "phat sounding chords" or whatever you want to call it and runs and stuff that sounds good to you.
Just like when you learned "Praise Is What I Do", I'm sure you played a chord and was like, "alright now, that sounds pretty good, I think I'll use that", that's what I do for most songs, a trial and error process is what I guess you can call it. What helps me even more is after listening to the song, I try to tell what key it's in (you can tell that most of the times (not all) by listening to the last chord in the song or it might be the chord at the beginning. Once I do that, I play the scale of that key to refamiliarize myself with what notes are played in that key, that way, I'm able to figure out what chords I'll be playing (like if you're playing in C#m (the key "I Worship You In The Spirit" by Deitrick Haddon, some chords you're likely to use are D#, F#, ect, based on the C#m scale (that's the relative minor of E major ...so it's the same as the E scale, you just start out on C#).
Often times, you can figure out what chord to play just by listening to the bass note, the bass note is often the root of the chord. But getting back to your question of how do you train your ear, just practice all your scales, major, minor, blues, and what other scales you like and become familiar with the sounds of each. Then practice your chords, play a major then a minor, see how they differ and make a mental note of it, then go on down the line with a diminshed or augmented chord and so forth. Once you do all of that put your eas to the test, try listening to a song and listen to what's being played do you hear the major, minor, diminished, ect. chords? Then from there you can learn the melody lines to a song, which is pretty easy to do, and from there apply all the other other thing I wrote to you above and what Hammondman, 4HisGlory said, as well as what other great advice you get on down the line, and then you'll be one your way to playing by using your ear!
