The best way, in my opinion, to learn a new operating system would be to use it as your daily machine at least for a week and perform all functions you usually do with your Mac/Windows.
Analyze what things are easier to do and what are not. You may also find things which are completely new to you such as some Linux only tools/softwares. When you run into problems with simple tasks like installing a basic software, google and find solutions for it. Start from there and keep learning as you go. Reading book for dummies as others mentioned will also benefit.