I am trying to move a game in to my Steam inventory, which is marked as "UNTRADEABLE You have to accept a trade offer WITHOUT this item first." So, how exactly do I do this? Do I select to "WITHDRAW" it, and then do some menial trade with someone else? Do I do the trade and it will automatically go in to my inventory? What are the exact steps, I can't find this described anywhere.

If you are purchasing untradable game from someone : Select the gift and click purchase, confirm trade offer in steam and after that game will be gifted to you. You can add it to your game library or save it in your inventory, as you want.
If you want to withdraw gift from your bot : Select gift and click Exchange button.