Quick answer
There is no one-device split-screen mode in We Were Here Tomorrow. The puzzles depend on the players seeing different information and describing it to each other.
Playing together in the same room
Use a device and game session for each player, keep both connected online, and join the same lobby through the in-game invitation system. Both players need access to the full game; see the Friend Pass explanation.
Keep each player focused on their own screen and make sure communication works for both. You should reach the same co-op session with separate Explorer viewpoints, rather than a screen divided into two panels.
Two controllers on one device
Connecting a second controller does not create a local second-player session. For different platforms, follow the cross-play guide.