The bottom of the adapter is a quill and it wedges inside your bike's steer tube just like a quill stem would. The top part is just a pole the same diameter as a steering tube would be if you had a threadless headset/fork. The threadless stem just clamps on the top part of the adapter the same as it would a steer tube. You likely need a 1" quill and 1 1/8" adapter part as most threadless stems clamp to a 1 1/8 steerer tube.

You can also clamp a 1 1/8 stem to a 1" tube by using a shim/adapter which are quite ubiqitious it is just a split tube and a lot of threadless stems come with them.