You will need the following:
1x 2.5mm (NOT 3.5mm) jack
1x 1/4" line socket*
Either 3 pieces of wire OR 1 piece of triple cored wire at least 6" long
An xbox 360 and controller
A microphone and headphones (to test)
I'd like to apologise for the lack of pictures as I forgot to have my camera hand as I was making this.
*You may ask why I've made a 2.5mm to 1/4" adaptor rather than to 3.5mm which is more common. Well, most karaoke mics are 1/4" by default and 1/4" to 3.5mm adaptors are more common than the other way round, so this seemed to make more sense.
Step 1: Step 1 - Wire the 2.5mm Jack
Step 2: Step 2 (optional) - Plait the Wire
Step 3: Step 3 - Connect the Line Socket
Firstly, remove the sleeve from the line socket and slide it down the cable ready for when the socket it connected.
Secondly, find the ground wire (this will be the one connected to the bottom most segment of the 2.5mm jack) and connect it to the ground terminal on the line socket. The ground terminal will usually be the biggest and will probably be part of the metal casing of the socket.
Step 4: Step 3 Conitnued
The xbox only outputs sound through one wire, the other being the line in for the microphone.
Plug in the headphones and pick one of the two unconnected wires and hold it to one of the terminals. If you've managed to pick the sound wire, you should hear a static/hum noise in one of the headphones speakers. This is the normal noise for the xbox headset. If you don't get this, then you've picked the microphone wire. Grab the other wire and put it to one of the terminals
You want to connect the wires so that you can hear the background hum through the right headphone. This is because a mono microphone outputs through the tip connector, which is the left channel.
Once you've identified the left and right channels, connect the microphone wire to the left and the sound out to the right. Before you solider them in place you'll want to run a quick test.