There are many approaches to learning how to use Galaxy. The most popular is probably to just dive in and use it.
Galaxy is simple enough to use that you can do many analyses just by exploring the interface. However, you may miss much of the power this way.
The Galaxy Training Network (GTN)
Thanks to a large group of wonderful contributors, there is a constantly growing set of tutorials maintained by the Galaxy Training Network (GTN) covering introductory tutorials, various scientific topics, development and administration.