How should one go about getting a job programming a large supercomputer?
Become a researcher in a field that makes use of lots of computing power, then specialize in the math modeling and simulation subfields. Surprisingly often it's quite easy to get time on a system if you apply as a post-doc or even a grad student. Becoming part of a research group that develops simulation tools for others to use can be an especially good way.
Or, get an advanced degree in numerical analysis or similar and get hired by a manufacturer or an organization that builds or runs supercomputers. On one hand that'd give you a much more permanent job, and you'd be mostly doing coding, not working on your research; on the other hand it's probably a lot harder to get.
But ultimately, why would you want this? They're not especially magical machines. Especially today, when they're usually Linux based, and the system developers do all they can to make it look and act like a regular Linux system.
If you want to experience what it's like, try this: Install a 4-5 year old version of Red Hat on a workstation. Install OpenMP and OpenMPI, and make sure all your code uses either or both. Install an oddball C/C++ compiler. Access your workstation only via SSH, not directly. And add a job queue system that will semi-randomly let your app run after anything from a few seconds to several hours.