Alright, there are many ways to do all of this. The video above is nice, but not something you really need to worry about with distributed audio and we'll go with the assumption they didn't blow a very basic color coded installation.
Each speaker has two wires connected to it with the volume control between. One wire is red, the other is black. Looking at the wall plate with all the binding posts, you see that you have 16 binding posts. The colors of them seem to be completely wrong, so odds are that they have just been mixed up for no obvious reason.
First, turn the volume controls all the way up in all the rooms.
Take a battery, and touch a wire between the battery and the top left binding post, and the binding post immediately to the right of it. Ask someone else to help you find out which speaker is making a bit of noise when you touch the battery terminal. There are only 8 speakers to choose from, so finding that speaker should be easy enough.
If there is no speaker associated with that connection, then touch the batter to the top left binding post and the binding post directly below it. Now see if you can find the speaker.
If you can't find it, you may want to pull the wall plate off the wall and see where the red and black wires run to. But, I don't expect this to be the case.
Once you have found the first speaker, get out a label maker and LABEL! That, or open up a program on your computer and take notes. Let's say the top two binding posts are the left speaker in your office. Odds are good that the next two binding posts down are the right speaker in your office. Check them out.
Repeat this process until you know where all those binding posts go to. You now have a good jumping off point.
What's next?
Well, you need to figure out exactly what you want from these speakers.
If they are small no-name speakers, then you shouldn't expect much from them. But, if they are better, larger speakers, you can expect some pretty decent sound from them. Now, speakers need power, so they aren't just going to work by you plugging your iPhone into the binding post. You need an amplifier.
You also need to figure out how many you intend to use at once, how loud you want them, etc. There are many ways to deal with this.
A decent way is to use a product like a Sonos amp and run that into a speaker selector. The Sonos can play back many types of audio, including audio from your phone. You can control the audio from your phone anywhere in the house using your Wi-Fi network. The amplifier in the Sonos isn't that powerful, but can run a small distributed system.
Plug the Sonos into the wall, then run it into a small speaker selector like this one...
http://www.ebay.com/itm/Niles-SS-4-high-end-high-power-Speaker-Selector-in-good-working-order-/281631111020?pt=LH_DefaultDomain_0&hash=item419285b76c
This is a quality unit. It accepts an input from the amplifier (Sonos) and will feed the speakers throughout the house properly.
Get a 50' or so roll of speaker wire (16 gauge, 4 conductor) and some wire strippers.
http://www.monoprice.com/Product?c_id=105&cp_id=10509&cs_id=1050903&p_id=7037&seq=1&format=2
and
http://www.ebay.com/itm/50-Feet-16-4-16-Gauge-4-Conductor-Premium-Speaker-Wire-Cable-FT4-UL-AWG-CL3-/271085260720?pt=LH_DefaultDomain_2&hash=item3f1df0cfb0
When it arrives, cut off a few feet, and plug the red and black wires into the RIGHT OUTPUT red/black connection on the back of the Sonos box. Plug the white wire into the red connection for the LEFT OUTPUT on the back of the Sonos and plug the green wire into the RIGHT OUTPUT connection on the back of the Sonos box.
Connect the other ends into the respective red/black inputs on the SS4 speaker selector.
From the SS4 connect speaker wire to the binding posts on the wall following this same process. Red to red for right speaker, black to black for right speaker, white to red for left speaker, green to black for left speaker. Do this until all 8 speakers are connected to the SS4.
Now, you turn the volumes back to 'mid level' at the walls, and you should be able to plug the Sonos in and start through the setup and rockin' the house.
