If I where to join the army and become a hacker what would my training and missions consist of?

Well, "hacker" is kind of a broad term. The information security umbrella covers a lot of specialties these days. What you're likely referring to is what we sometimes call "penetration testing", which is probing applications and systems for security vulnerabilities. If this is what you're interested in, then you need to be very good at programming. Not just in the sense that you can crank out code to meet particular requirements, but a deep understanding of what's happening inside the system. Most aspiring pen testers would be well served to get at least a BS in Computer Science. I know that some people try to go the "Information Systems" route, but that's geared more for system administration instead of programming, which is far less important in pen testing.

As for me, I tried being a hacker and found that I wasn't suited for it, both skill-wise and personality-wise. It turns out, I enjoy hunting for bad guys and investigating weirdness. Since then, I've spent most of my time involved in intrusion detection and other roles related to incident response. I started down this path while in the military, and I'm still loving my work.

I suggest you start off by doing a little reading about the different information security specialties before deciding that you want to be a "hacker". Infosec is a fun and rewarding field to get into, and depending on the specialty, the military can be a great way to get initial training.