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If you're new to Subversion, the first thing you want to do is learn a little about how it works and the general commands. We recommend that you first get familiar with Subversion in the command line, then move on to the GUI clients. This will help you make the right decisions as you start to use Subversion on a daily basis.

There is one excellent place to start:
http://svnbook.red-bean.com/

If you don't want to read the entire book, you can skip ahead to a few important chapters.

Subversion in action
Basic work cycle

Once your are comfortable, you should learn about the power of Branches, Tags, and Merging.

Branching and Meging

After learning the basics, download and install a Subversion client on your computer.

We can recommend a few for both Windows and Mac OS X.

Windows

TortoiseSVN
Probably the best client for Windows.

Mac OS X

Textmate (built-in bundle)
Perfect if you already use Textmate

SvnX