You just have to DO IT!
Start simple. For example: listen to some hymns that have been recorded and try to duplicate what you hear one note at a time.
I say hymns because they all have such simple patterns and progressions, they are the easiest to master.
Get a tape recorder and record yourself trying to duplicate what you hear. When you listen back, you'll hear little subtilties that you may have missed trying to play and hear at the same time.
GRIND IT OUT. There is no shortcut or substitution for hard work.
Then, after you've done your best to learn a song on your own, either ask someone better than you or visit websites like this one or gospelkeyboard.com, or earnestandroline.com and see how the song really should be played in order to fill in the blanks.
It takes a lot of time to really train your ear and your hands to duplicate, so don't give up if it don't seem to be working right away.
And, be sure to press through and learn from negative comments from people. I have found that the biggest critics of people's playing ability are people that can't play themselves and have absolutely no idea how hard it is.
Stick with it