After completing the first mission inside Dr. Loboto's mind, you will come to the Psychonauts HQ. Take the elevator behind the receptionist to get to the main hall. You can freely explore the main hall first, or head straight to the "Classroom" door and down the hall to find the Otto-Matic that you will need to use.
When using the Otto-Matic for the first time, you will be taken through a short tutorial showing you it's menus, part of which includes receiving a PSI Core and the PSI Cards needed to combine them together for free. Finishing the tutorial inside the Otto-Matic should earn you the Achievement.