This act begins when you talk to Snakeman. It seems that the Master of Shadows has a new plate, and needs your help to get it activated. After talking to the Master of Shadows, you'll be given the option to talk about shards, which goes to the Soul Shards: the Sequel quest, or to talk about plates. You learn that the new plate is incomplete: it needs another piece called an Old World Stone in order to be activated. He also tells you that you will need a demon level 12+ for the assignment, and sends you in route to the Junkman of Suginami, the route to which will be displayed for you. Afterwards he hands you 5 Ariadne Stones, which allow you transport anywhere you like. (But, since they're a sample, anywhere you like within Suginami.)
Use one of the stones to go to the Junkman (or don't, but they're not all that useful since you can only go to a select few locations), and here you'll find out why you need the level 12+ demon. It seems that the Old World Stone is very common within the mines...but only your demons can go in and get them. He also tells you that you'll have to send them in alone, and that they have a percentage chance of either getting the stone, or getting lost in the mine forever. (I personally did this with a level 13 pixie and had a 70% chance of success, which was successful for me. I'm guessing it's probably 60%=12, 70%=13, 80%=14 and so on.)(This player of Imagine tried a few demons of varying level from 12-15, and can safely say that the success rate is always 70%.) When you demon is successful, you will be given the stone, and the demon will be given a 30,000 XP bonus from "fighting inside."
After returning to the Master of Shadows with a demon over level 12 (probably not the one you just used in the mine) and the Old World Stone, you will be able to make the plate by sacrificing the demon that you just used and the Old World Stone.