Hi James,
The link here should give you most of the information you need:
http://pdf.crse.com/manuals/3043534111.pdf this shows all the connections you need to make from the back of your c33r radio.
As far as the amplifier is concerned, you usually have 3 wires that you need to connect (in addition to the red and white phono plugs that carry the audio information from the LINE OUT of your c33r).
The three plugs are 1. Power (+12V) directly from the battery of the car, and this must have a fuse at the battery end. This is usually a thicker cable because it has to carry enough power to operate the amplifier safely and it is usually yellow in colour. 2. Earth (-12V) of the same thickness as the power cable and is connected to the metal bodywork of the car near to where the amplifier is installed (usually black in colour). 3. Is the remote lead you mention and is connected to the 'AMP REM' lead on the back of your c33r (usually blue/white striped) - a wire the same gauge as this to run to the amplifier is OK.
What the remote connection actually does is tell the amplifier to switch on or off to coincide with you switching your c33r on and off - you can't bypass it otherwise it won't work.
You can often buy amplifier wiring kits from specialist car radio dealers (they should also be able to advise you what size (gauge) of cable you need to install your particular amplifier safely), but if you are in any doubt I'd always recommend getting one of them to fit it for you - it's not a big job so not too expensive and certainly better than damaging your gear.
Hope this helps.
