Here's a quik rundown of how to hook up a sidechain on mac.
In this example I have two tracks. One containing a vocal, the other containing some music. I want to sidechain the vocal to the music. In other words, I will duck the music using the vocal.

1. Add ReaComp on the music track.
Find "Detector Input" in the FX window and set it to "Auxiliary Inputs L+R". This tells ReaComp to react to whatever comes in via that input, as opposed to reacting to the music which will be on channels 1 and 2.
Set the threshold to -25dB for now.
Set the ratio to 8:1 for now.
These are fairly aggressive settings. You might not want to keep them, but with the majority of source material, they should ensure you can hear the compressor working once the routing is right.

2. Move to the vocal track.
Hit Control+3 and move down to sends.
In there, select the music track.

3. While still focused on the vocal track, hit the letter I to open the I/O dialog.
Open VoiceOver's item chooser with VO+I. 
Type "send", find the send you made to the music track in the previous step. hit enter to move VO focus to it.
Navigate to the right with VO right arrow until you find "destination audio 1/2", and change that to 3/4. This connects the send to ReaComp's auxiliary input (remember, you set ReaComp to listen to that back in step 1).
If you don't see 3/4 in the list straight away, choose "New channels on selected track" first, then you'll be able to choose 3/4.

Now the vocal is being sent to the music track on channels 3 and 4, which feeds it into ReaComp's auxiliary input and engages the compressor.
Adjust ReaComp's Threshhold, Ratio, Attack and Release according to your needs once you've gotten the routing going.

If you do not want to hear the vocal track (sometimes it can be useful to hear how the compressor is reacting on its own), hit Ctrl+3 on the vocal track and turn off "Master parent send".

Ducking music under a vocal is just one example where sidechaining is useful, but the workflow is the same no matter what you want to sidechain. At least, it is when using Reaper's stock plug-ins. Third-party plug-ins can be a different story and would have to be dealt with on a case by case basis.

Writing by Jenny K, assorted uninvited pedantry by Scott. We hope it's useful. :)