Wow, I actually had no idea; how is this all pre-planned, does somebody at NASA just put "67-P/Churyumov" into a "Orbital Maneuver Planner" and let some computers crunch the possible paths out? Or does someone actually sit down and come up with the possible sequence of orbital assits (to later verify with a computer) with a pencil and paper?
It's a combination of both. They have tools that help worth the trajectory calculations, but they have to manually decide on the basic layout of the path to take.
There is a very interesting interview with Pablo Munoz from the Bepi Colombo team about flight dynamics on the Omega Tau podcast that explains this: http://omegataupodcast.net/295-bepicolombo/
The other interviews on the same episode are also worth listening to. In fact, the entire podcast is great.
Common orbits are solutions to the two body problem, but Shane Ross has a few videos on youtube about chaotic solutions to the three body problem, allowing objects to move in very complex orbits with very little fuel. This has been used for a few missions as I understand it, the math is WAY above my head, but the video is still quite watchable with lots of cool orbit animations:
