For certification the best you can do is to understand how the products really work and to use them.
When you purchase the software there are books on each of the CDs, User Guides and the like.
This is the basic how the product works.
Then you'll learn a lot from trying things out and breaking them in a lab environment.
If you buy any Tivoli consultancy then you'll learn a lot from seeing how those guys go about setting up your environment.
With Tivoli it is now a huge product range, so if you really want to understand a particular area then you will be better off looking in detail and using the products; if you're at a level where you need to be able to manage an implementation then you'll just be needing the concepts from User Guides etc.
Also, there is Tivoli training now available from various companies. This will still usually only get you going with the products, IMHO it won't cover all the bits that don't work, and the associated workarounds.
The Tivoli support site has got a lot better recently when you have issues.
Unfortunately, the scale of these products isn't the same as the Microsoft or Netware or Cisco, so the range of books is much more limited. And I haven't seen anything about "how to pass certification" - except for the sample test on Tivoli site.
And be warned, the exams will be updated for 3.7, and from the look of it the update will be a big one, meaning that it is even more important to understand how the product works, rather than how the book says it works.
Its a lot of waffle I'm afraid that is basically trying to say that there isn't an easy answer to this. You need to dig around different resources for each particular issue that you're after.