In the film Twelve Monkeys, they show Cole traveling back to the past but not how he returns to his time. Is the process ever explained?
This isn't explained in detail in the movie. But IIRC, the scientists control Cole through a device in his tooth. The second time they try to shift him to 1996, they mistakenly place him in the middle of World War 1 and then are able to move him forward by 80+ years to 1996. We can therefore assume that they can control Cole's position in time remotely.