The Dimensional Rift is the tear between the Tower and Herumon Dungeon. From floor 100 you can send a copy of a creature through: free, once per creature, it arrives in the Dungeon at level 1 with its grade and mutant status, and the Tower keeps yours. The rift opens in the Steam client - the web build can only look in.
1A locked plate until floor 100
DIMENSIONAL RIFT is on the menu from the start but dark, with OPENS AT FLOOR 100 under it. Beat floor 100 and the plate lights.
2The rift window
Once open, the window explains the crossing and lists your WORLD TRAVELERS - every creature you have sent through so far.
3SEND THROUGH THE RIFT
Open a creature's sheet from the Inventory. From floor 100 its header has SEND THROUGH THE RIFT; click it and a copy crosses to Herumon Dungeon. The rift runs one way - nothing comes back - and in the web build the button only tells you to use the Steam client.
4The World traveler mark
A creature that has crossed carries the World traveler mark on its sheet, is listed in the rift window, and cannot be sent twice. Sending your first earns the Dimensional traveler badge on your profile.
Screenshots are taken from the live game by tools/tutorial_shots_b.py (dfmc-client) and regenerated after interface changes. The rules behind each screen: system-client-shell.