How to have an Arduino communicate with 3 other Arduinos?
You could use: U(S)ART, I²C or SPI. You should check this post for information on these protocols.

Some quick googling gave me this:


SPI: mainly for high data rates, approx 25 MHz clock but only bus has to be on same voltage level, single master (can be done through software), data arbitration not possible.
I2C: mainly for control and low data transfer (limited by bus capacity, etc...), but can be interfaced to different voltage levels and multimaster bus environment, inbuilt arbitration etc...
UART: single P2P comm, 115 kbps max.


http://www.edaboard.com/thread53139.html

I don't fully agree with it. You can send via UART to multiple devices, but then you have to handle the addressing in software. But other than that, UART is very easy to debug as Arduinos often have an USB connection.

"I²C is somewhat complicated at the physical level, but all that complication is handled by the hardware (the TWI interface of the AVR chips). At the user level, it may be the simplest to use". I don't yet have a lot of experience with this protocol, but if you want to use it, check out the other answer.

SPI would be a fair shot as it does enable master with multiple slaves in its standard.

Summary:

All protocols have different pros and cons. It's not really up to us to choose one for you. And you should look them up and learn about them by yourself.

Then try to choose which one applies most to your needs, and get started with that protocol. They are well documented and if you really can't get out of it, you can post another question ;D