You can read all the nitty-gritty details in this tutorial, but the gist is basically the following:
$ git svn branch -m "Topic branch" my_topic # Create SVN branch called "my_topic"
$ git checkout --track -b my-topic remotes/my_topic # Create the Git branch for "my_topic"
# Hack hack hack...
$ git svn dcommit --dry-run # Make sure you're committing to the right SVN branch
$ git svn dcommit # Commit changes to "my_topic" branch in SVN