I have 4 fans in the same room If I install the necessary piece in each fan, can I then use 1 remote for all or do I need all 4 remotes?

You can, but what often happens, even with just 2 is, 1 May receive the signal, other won't, then they are out of sync(Pressing the light button may turn 1 on, and turn the other off).
Then you have to try to get transmitter to be received by 1 to get back in sync. With 4 this will be tougher.
Try it, If you have a good strong signal, you may not have a problem.
Good Luck

I recommend against using remotes, especially for multiple fans. Just use wall controls.

Ceiling fan remote controls, remote kits, speed controls, dimmer switches and more - at Ceiling Fans 'N More (http://www.ceiling-fans-n-more.com/ceiling-fan-controls.php)