How long do you need to hold a baseball?

Long enough for the fielder to demonstrate to the official(s) that he has control of the ball. If he drops it 'during the course of fielding' it's deemed not a catch.

If it is deemed, by the ump, to be dropped in the transfer from glove to throwing motion you won't have held it very long, but it is a judgement call and may go against you. The same for catching a fly ball, its upto the ump. Just don't drop it!_________________________________________________________________________________

A fly ball is a term for when the batter hits the ball and it goes high in the air, and usually makes for an easy out because they are easy for outfielders to catch