A good jazz teacher would be able to lead you through this, or a classical teacher that has a composition background.

You'll need to learn all your chords of course. Take a few keys every day and just practice your four triads for each (major, minor, diminished, augmented) with their inversions up and down. Use a metronome and increase the speed weekly until you've got all of them going at a decent pace. When you can do that, then you can move to the four part chords and do the same. Everyone teaches it differently, but my teacher had me doing 10 of them -- maj6, min6, dim7, maj7, dom7, min7, min7b5, minmaj7, augmaj7, aug7, in that order, with their inversions, in closed and then open position, in all 12 keys. It takes years honestly.

And of course you'll want to be playing songs from lead sheets -- over time you'll start picking up on the ii-V-Is, I-vi-ii-Vs, and I-IV-Vs, etc.