What is the ruling about losing a shoe when the ball is still in play?
Can the player still play or does he need to get it back before continue playing?
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There is no rule I can find in the rules of basketball that says a player must remain shod (shoed?) during play of the game while the ball is live. Therefore, a player who loses a shoe must stay on the court until the next stoppage (timeout or foul call, usually). They are not allowed to leave the court to put the shoe back on (that's a technical foul for too few players on the court). They may move to the side and try to put their shoe on, or they may continue to be part of the play, but if you try running along a basketball court and then suddenly stopping or changing direction with a stocking foot you'll realize there's just no way, especially for a forward or center who has to maneuver in traffic. A shooting guard, maybe.
What should happen is the player's team should get a stoppage of play; get hold of the ball, take a 20-second time out, let the guy put his shoe on or bench him. However, that doesn't always happen immediately:
http://www.youtube.com/watch?v=vRd6welKAYI (IMO that should have been a technical)
The NBA has no rule whatsoever about what happens if a shoe comes off.
This was vividly illustrated on Dec 13, 2014, GSW @ DAL: Marreese Speights lost his shoe. Stephen Curry then later tried to pass Speights his shoe, whereupon Tyson Chandler deflected it out of bounds (YouTube).
I do not know about the NCAA or FIBA.