Well, some of them never got in the habit of relying on sheet music in the first place
It seems to me, in my attempts, that a great part of the trick is to be willing to enjoy being a beginner again. I was always surprised when I'd sit down and just noodle - I didn't really think I could, and I was pleasantly surprised.
But to actually learn to do it with ease takes the same kind of time and commitment as learning to play with sheet music did, and there's distinctly a learning curve, which is why being willing to enjoy it is important. I actually think going cold turkey for 6 months or something is the best idea, tho I've never done that. But I do play from lead sheets and can do some rudimentary improvisation, and sat down this eve and played Tennessee Waltz in 4 different keys, and played without sheet music at jam tonight, so I've come some ways.
What was a real revelation to me (and I am admittedly an intermediate piano player) is that it's *all* about the *sound.* I hear in a whole different way than when I was only reading notes (and I know there are classical players who hear well). So the best advice I ever got was - listen, listen, listen.
One way to start is to team up with another musician who can play the melody while you accompany - a flute player, or violinist maybe - and play simple songs you both know. I accompany dance music, so I learned to read a lead sheet. But I think again, enjoying it is key, because it isn't always going to work right off the bat. You can start with just using block chords, or even just a tonic, as accompaniment. Then try simple patterns - all the LH patterns from Canon in D are useful in playing accompaniment or lead sheets
Another way is to join one of the study groups in the ABF - jazzwee has a great one on how to begin to play Autumn Leaves, here:http://www.pianoworld.com/forum/ubbthrea...ite_id/1#import
There's another one called "How to play from a lead sheet" and one on "Pop Piano Pro."
And then there's always - pianomagic. It's an on-line play-be-ear course. A search in the ABF will bring up *many* threads. But again, being willing to be a beginner is key. Rosanna, a fairly accomplished player, made the decision to do it the pianomagic way, and she's played some lovely by ear and improvisations in the piano bars and recitals. Several people there - Seaside_Lee and mahlzeit for instance - learned to play piano that way. But Seaside spent 3 or 4 hours a day over the past 4 years, just like good classical pianists do.
It's also interesting to read Mr. Super-Hunky's take on it - he reads, but slowly, and improvises all of his pieces, and he does lovely work. He says over and over that it's about finding out where on the piano the sound you want comes from, and spending the time to explore it.
But I think it really comes down to being willing to take the risk, and be a beginner again, and enjoy it, and not give up as you work your way thru the study groups, or figure out the chords with a friend, or ask questions in the forums at pianomagic. It's really liberating, though.
That's my take on it, any way.