user3289: I'm pretty new to this whole thing so please excuse my lack of familiarity with terminology.
I'm looking to build two "buzzers" of sorts. One will live on the ground floor and the other will live on the fourth floor. There is wireless internet as well as wired internet available to connect the two. 
This is the basic idea. I might put more frills in later. Both buzzers have one button and one LED. I want it so that once a buzzer's button is pressed, the LED lights on both buzzers will light up. Then, only when buzzer two's button is pressed, will the LED lights on both buzzers turn off.
I'm pretty tied up on the two Arduinos communicating with each other. Is it possible to do something like that?

user1566: Wired
Communication speed is not a factor - you only have to transmit an on/off signal. The simplest method would be to run a 4-wire cable, like a telephone cable, between the two.
The wires would be

GND 
5V (maybe) 
Ground floor output -> fourth floor input
Fourth floor output -> ground floor input

The steps are

Both wire 3 and 4 start LOW When ground floor button is pressed, ground floor led goes on, wire 3 is set HIGH. 
Fourth floor is monitoring wire 3, when it goes HIGH, fourth floor led goes on, and    wire 4 is set HIGH 
Ground floor is monitoring wire 4, when it goes HIGH, ground floor led goes off, and wire 3 is set LOW 
Fourth floor is monitoring wire 3, when it goes LOW, fourth floor led goes off,    and wire 4 is set LOW 
Ground floor is monitoring wire 4, when it    goes LOW, it begins waiting for a button press again.

Wire 2 can be used for 5V (or 3.3V depending on the Arduino) so that one of the devices can be powered off the other.
Wireless
The other option is to attach an RF transceiver to each Arduino, something like this would be good as it has 100m line-of-site range which you might need to get through 4 floors of concrete.
Learning
Start off with the simple wired method shown above. When it is working, connect wire 3 and 4 into the RX and TX pins and try to communicate using the serial port. Finally, move on to the wireless transceivers.

3289: <p>I'm pretty new to this whole thing so please excuse my lack of familiarity with terminology.</p>

<p>I'm looking to build two "buzzers" of sorts. One will live on the ground floor and the other will live on the fourth floor. There is wireless internet as well as wired internet available to connect the two. </p>

<p>This is the basic idea. I might put more frills in later. Both buzzers have one button and one LED. I want it so that once a buzzer's button is pressed, the LED lights on both buzzers will light up. Then, only when buzzer two's button is pressed, will the LED lights on both buzzers turn off.</p>

<p>I'm pretty tied up on the two Arduinos communicating with each other. Is it possible to do something like that?</p>
 1566: <p><strong>Wired</strong></p>

<p>Communication speed is not a factor - you only have to transmit an on/off signal. The simplest method would be to run a 4-wire cable, like a telephone cable, between the two.</p>

<p>The wires would be</p>

<ol>
<li>GND </li>
<li>5V (maybe) </li>
<li>Ground floor output -> fourth floor input</li>
<li>Fourth floor output -> ground floor input</li>
</ol>

<p>The steps are</p>

<ul>
<li><p>Both wire 3 and 4 start LOW When ground floor button is pressed, ground floor led goes on, wire 3 is set HIGH. </p></li>
<li><p>Fourth floor is monitoring wire 3, when it goes HIGH, fourth floor led goes on, and    wire 4 is set HIGH </p></li>
<li><p>Ground floor is monitoring wire 4, when it goes HIGH, ground floor led goes off, and wire 3 is set LOW </p></li>
<li><p>Fourth floor is monitoring wire 3, when it goes LOW, fourth floor led goes off,    and wire 4 is set LOW </p></li>
<li><p>Ground floor is monitoring wire 4, when it    goes LOW, it begins waiting for a button press again.</p></li>
</ul>

<p>Wire 2 can be used for 5V (or 3.3V depending on the Arduino) so that one of the devices can be powered off the other.</p>

<p><strong>Wireless</strong></p>

<p>The other option is to attach an RF transceiver to each Arduino, something like <a href="https://www.sparkfun.com/products/691" rel="nofollow">this</a> would be good as it has 100m line-of-site range which you might need to get through 4 floors of concrete.</p>

<p><strong>Learning</strong></p>

<p>Start off with the simple wired method shown above. When it is working, connect wire 3 and 4 into the RX and TX pins and try to communicate using the serial port. Finally, move on to the wireless transceivers.</p>
