This is a complex question. Let's answer it with a few more questions:
1. How many zones do you have? (rooms with speakers)
2. What equipment is already in place? (ex. the wallplates with CAT6, any labels or brands?)
3. What do you want to do?
4. What is your budget?
The number of zones will tell you how many channels you need on the amplifier. The brand of equipment will tell us how it's setup. For example, CAT6 can be used in a variety of ways:
1. As speaker wire
2. For data transmission (ex. to send an input to the amp)
3. For control (send & receive signals for things like volume)
The most basic setup is a whole-house amplifier, something like this:
http://www.parts-express.com/dayton-audio-ma1260-multi-zone-12-channel-amplifier-60wpc--300-8150
They also have wireless solutions, which offer more flexibility:
http://www.sonos.com/products/wireless-stereo-components
At the most basic level, you need two things:
1. Power for the speakers (via an amplifier)
2. A source signal for the speakers
You can do one big amp like the whole-house unit above, or individual amps per room. For getting the source in, you mentioned there's a source input in every room. You can plug in an iPod or CD player into that & play it in that room, but you can also go one step further by getting something like a Sonos where you can send inputs to other rooms & also use network inputs like Spotify via a smartphone, tablet, or computer.
The more complex you want to get, the more the price goes up. So we need to figure out how many zones you have, what hardware is in place already, how you want to use it, and what your total budget is. For example, Sonos is by far the best wireless system (which can still apply to your system even though it's wired, because you can relocate inputs to other rooms for playback), but it's $500 per amplified unit, so if you have 10 rooms, that's five grand right off the bat.