Pleasant conversation. Be open and admiring of the things you like. Be social and polite. Try to be sticky.
"Say, you seem to gotten some of my shadow on your backstory. Why don't we try some of my backstory on your shadow? Mmm. Delicious."
Hopefully you've had a chance to read Ginger's answer as it covers Everyway. Nice midwife process there.
In Strange Bedfellows, the players spent quite a bit of time cross-linking their Characters with back story. That's a sweet deal if you can get it too. Of course, this is harder when you bring in new characters.
But then, again, see Ginger's post about Everway.
Many Players are 'develop in game' types. Especially gamers that have a road of experience behind them—for they've done permutations of the hero in there own mind. The world helps create a hero that fits the world better.
This gets the GM more involved, more invested in the PC, even as the Player is more sure of the PC right from start.
Everyone can try to think "yes" in respect to the new Character rather than think "no, that wasn't quite what I was thinking."
With that segue, I offer you this link to an article by Pete Darby.
Improvisation techniques for gamers
Shed your fears and open your mind to better play
By Pete Darby