Open up your case.
You should see cables running from the front panel to the motherboard. On the motherboard you will see a multi-pin connector. What is your exact ASUS motherboard model? Here's a generic ASUS one. You will see this on the motherboard where the front panel connects to the board. A bunch of pins will terminate here.
Notice the pin labelled MIC. You will see GND etched on the motherboard. Use this to orient yourself. The Mic one is just below the GND pin. Connect it here. Notice the entire top row is devoted to FP_Audio or Front panel Audio. There are other places to connect it (e.g., if you just want stereo sound, there's a left and right FP_R and FP_L).
Move the mic connector over to the Mic pin if there is one. If not, you can get a cable at your local computer supply shop. As you can tell from the others, they are very basic wires with simple terminals.