The first thing I would do is read the TSM Administrator's Guide. It's like taking the courses. If you know that guide well, you'll pass the certification exam IMO. The one thing I struggled with is it seemed like the first 6 months I was full of information on what I *could* do with TSM, but not enough exposure to environments to know what sorts of best practices people employ. In some cases, it's clear what the best practices are because IBM publishes them. In other cases, it's not so clear. e.g. do you create many domains, management classes, policy sets? Do you create many storage pools? Or keep as few as possible? Is it better to create many smaller TSM database files for your storage pools or fewer larger ones? I started with the KISS principle and always defined as little heirarchy/complexity as needed but over time, having seen many environements, I now have a much better sense of when it makes sense to do things like that.
I guess all in all what i'm saying is TSM is a highly configurable product. So much so that when you're first exposed to it it can be a bit overwhelming. Only time and experience will help you there.. On the plus side that same configurability makes it incredibly powerful in the right hands.
Download and read the admin guide. It will be your bible:
Then any client and database guides for whatever clients and databases you have to support.
Taking the certification exams can help you expand your knowlege too. Do it once you're somewhat comfortable with the admin guide. The act of taking them will force you to think about scenarios that aren't necessarily clear. You'll probably fail it once or twice before you pass it but along the way you'll learn a lot.
So that would be my strongest recommendation. Read the guide(s) and take the exams. The two together will get you up to speed quickly.