Get the grasp of a big system of applications and skills

Question

I work for the IT department of a big company with lots of applications. Usually my day starts managing custom apps, most of which I barely know, and fixing single problems on them. The problem is: for each problem on a different application the startup time is high and my effectiveness in resolving the problem could be better if I knew better the application itself.

Question:
Are there techniques (better if established ones) to understand a big ecosystem of software and learn the most important parts of it both from an IT and operational point of view?

Side quest:
Is there some software which can help me in the process? (eg in the task of discovering, organizing information...)

Answer 1

Imho, good searchable program for storing and organizing information is absolutely essential here

I am using Keynote NF (freeware: tabbed notebook with RichText editor, multi-level notes, ability to paste images and more) - you can use it to organize and store information; paste screenshots from these applications etc

Answer 2

I think the best thing would be to have someone who knows the system well sit down next to you as you work and answer your questions for a couple of hours a day. This person will need to be assigned by your boss and they will need to have some time allocated in their schedule. I've found working with a mentor to be something like 10x faster than flailing around on my own.

As for software, I like to use Notational Velocity (OS X) and Graphviz to organize information.