I don't know too much on how this technology works, so can someone explain to me where I need to plug the headset into the motherboard in order to hear audio through the headphones but still speak through the microphone?
This would depend on which type of connector the headset has. Common types are USB, four-pole 3.5mm jack (these are usually made for consoles and laptops), two three-pole 3.5mm jacks (usually made for desktops).
Most manufacturers describe how to connect on the box, in the manual and on their product page.
I had trouble with hearing through my headset/speaking through my mic at the same time. I realized I needed to get an audio splitter. This splitter should have 2 ends that connect to the in audio and out audio (in my case, it was near the motherboard on the outside of the case). On the other side of the splitter, there should be 1 female end that connects to the headset.