Everything that piecesparts just stated is 100% on point (great post, man!)
I used to work at an install shop in high school. Always use a dedicated power wire for your amps. 10 gauge power wire is sufficient - do not run it on the outside of the car. Perfect installation would be like this: run a 10gauge wire from the battery, through the firewall (be sure to use a rubber grommit! Greenlee knockout punches are great for making perfect holes in a firewall) and back to the amp. Be sure to: 1) debur your hole and use a rubber grommit to keep your wire from getting cut and grounded out and 2) Be sure to use a circuit breaker or fuse WITHIN 18" FROM THE BATTERY - this is super important just incase the power wire DOES short out somewhere (unless you like your car burning down
).
With that said, you'll run your power wire from the batter to the amplifier - don't tap off of the radio power wire. Run a stranded 16-18 gauge wire from your "remote turn on" or "power antenna" lead on the back of the stereo back to the amplifier's "turn on" power feed. This will make sure the amp is only turned on when the radio is on - use this unless you like your battery dying.
Last, be sure to ground the amp properly unless you like lots of ground noise (alternatore whine, etc.). strip any metal from the place it's contacting. Mount to a shock/strut tower or something that attaches to the frame, not just to a body panel.
There are two basic types of signals you need to understand: "amplified" or "speaker level" signal - this is the powered signal that your radio puts out to the speakers directly using the supplied speaker cables. then you have "non amplified" or "line level" or "low level" signals. This signal has little to no power and is what you want to feed into an amplifier - you should have RCA outputs on the back of your stereo that will put out this low level signal. If not, there is a company called "PAC" that sells line-level converters, they will turn a speaker level output into an RCA output. I wish it was as easy as just splicing an RCA into a speaker wire, but it ain't
. I can link you up to one of these at Crutchfield if you want to get one cheap.
You should use the RCA outputs on the back of your reveiver if possible - assuming yours has them. It is not suggested to run a "speaker level" signal into your amplifier or you'll get the distortion spoken about above. You should try to always run RCA's where possible. If your amplifier has a "speaker input" on it, I guess you could go ahead and use it. I still wouldn't recommend it. Most of your better equipment won't have features like this.
I suggest 14 gauge wiring as a minimum for any speakers that are being powered by an external amp. Sure, you can use some chintzy ass 18 gauge wire - it will work, but your overall stereo system is only as strong as its weakest link - so, why would you buy an external amplifier to increase power only to choke out the sound using cheap ass wire? Wire should be your biggest expense consideration when piecing together any sound system. Buy good cables - good power wire, good RCA's, good speaker wire, good ground wire. In most cases, going big is your best bet.
For reference, one 10 gauge power wire is suggested for each amplifier. If you need to run two amps, but only want to run one power wire, you can buy trunk-mount power distribution blocks at your local stereo shop. For two amps, run a single 8 or 6 gauge wire to the location the amps will be and split it into two ten gauge wires using a distribution block - the 6 or 8 guage will carry enough power to allow you to cleanly split the power equally between both amps with no loss (if you use one 10 gauge and split it into two ten gauge wires, you're only getting half the power to each wire!)
Lastly, never run RCA (low level or line level) signal wires anywhere near a power wire. Try to keep your speaker wires away from your power wires. For example, never run your RCA's or speaker wires bundled up with your amplifier power wire. This is a big no-no, you will be able to hear electrical noise if you do things like this. Try to run all of your power wires down one side of the car and all of the speaker/signal wires down the other side.