For single entry (which I assume yours is), all you would need to do is cut off a section of Cat cable ~1 ft (make it 2 to be safe) longer than the overall length you want for the finished cable.
Assuming you want to just use the bare wires inside the cat shielding, pull out all of the wires inside that shield.
Now, thread the cable through the headband (or wherever it threads) from the entry side to the non-entry side (right to left, assuming all of your wires go to the right headphone and that's where the jack comes out). You will need 2 sets of wires to do this. One pair will be for Left signal, the other will be for ground. The ground cable only needs to go as far as the right cup where it will be soldered together with the right ground. Most single entry headphones will have a place for this to happen (the ground comes in through the wire to a pad, then another cable goes from that pad to the other headphone; check to make sure on the existing wires, if you can, to see if the left signal does that too).
Thread those left wires through the cable hole and leave them be for a bit.
Now, solder up the common ground (like I talked about before) and thread those through the cable too.
Lastly, thread the right signal in and solder it up.
Now at the other end of the wires, trim them all so they're the length you want the final cord to be. If you're going to sleeve them, now is the time to do so. Unscrew the plug you bought and thread everything but the part you'll be soldering onto the wire (if you don't do this, you will have to desolder and do it again...trust me). Then start with one of the pairs of wires (make sure you write down which color is going to be what) and solder it to the appropriate place on the plug. Do the same for the remaining wires.
Most often: T
ip: Left Channel R
ing: Right Channel S
leeve: Ground. (that way you'll know what people mean when they say TRS plug). You should be able to tell which of the 2 front connectors goes to the tip (it will be connected to the center).
The mic should be the same basic method. I've never done a mic cable before, but it shouldn't be hard to do.
If you're going to do any type of braiding of the wires, do it before you start to solder the plugs on (label or write down which is which beforehand) and before any type of sleeving goes on. Google Litz braid for a good how-to.
You could double the ground if you so choose. Some people recommend having the number of ground wires be equal to the number of left channel + number of right channel wires (4, in this case).
Hope that helps, sorry for the giant post if you already knew this Edit
: I definitely see where Tjj226 Angel is going with this, and he may be right. I've never used Ethernet wire for headphones, so I was just going off of what I do know. Either way will get you the same result: Working headphones, the choice of method is really up to you at this point.
You could even get fancy and go buy a couple of jacks and mod your headphones for a removable cable if you so choose. Once I'm done with my K240s, I think I may do just that with a few older pairs I have lying around and possibly get up the courage to do it with my DT770s.Edited by liquidzoo - 1/31/13 at 8:08pm