That's an interesting question. And not an easy one!
It all depends on what you like. Reading your message, I'm guessing you're not a partner, so you don't get a lot of occasions to work on different projects and learn different aspects of storage, this would be a great way to learn.
Personally, I always had a problem "learning". I mean, learning as an activity of its own. I always needed real projects to work on, and was lucky enough when Santa delivered some 20+ blade servers and two NetApp filers and said "You're the guy that is going to set that up because no one else knows NetApp"... I didn't know NetApp either, and I had great fun.
If you are like me, and can't get motivated on purely academic work, that's going to be tough, but you can certainly find some activity :
If not NetApp, I'm a virtualization guy, so I spent a day or two setting up a VMware / NetApp lab on my laptop with VMware fusion and the NetApp simulator. Maybe that's something you would enjoy doing : install the whole stack, install VSC, have fun with our efficiency stuffs with VMware's VAAI for NFS
You're more a microsoft guy ? Go Hyper-V, cDOT and SMB3 integration with copy offload
By the way, if you don't know the NetApp Simulator, it is time to head to the download section of the support site and install it, this is a huge learning resource by itself.
If you need to work on existing environment, play with OnCommand Core / Ops Manager. Configure alerts, make sure everyone is healthy and you get an email when storage gets low or latency goes high.
Jump on that guy trying to solve a NetApp problem, get involved with support, like you said, troubleshooting is also one great way to learn, you start by asking stupid questions and you learn by the answer... if the guy you're talking to has enough patience!
Work on documentation is also a great way to learn a lot of things : even the obvious topics requires some work to simplify and explain to whoever is going to read you. I've had fun working on a screencast to explain SnapMirror between 7-mode and cDOT (here). Documentation is nice because :
1/There is never enough, you'll always find something to document
2/It requires you to dig as deep as you can to explain what you're working on
3/Anyone can do it, it is not about how technical you are, the topic may be simple, it is about how good you understand it, and if you can explain it, there are chances you can climb the ladder one more step.
4/It is a great occasion to get review by your peers
These are my two ¢ !