How do I create a new branch?

Right click and open SVN Repo-browser:

Right click on Trunk (working copy) and choose Copy to...:

Input the respective branch's name/path:

Click OK, type the respective log message, and click OK.

Branches in SVN are essentially directories; you don't name the branch so much as choose the name of the directory to branch into.

The common way of 'naming' a branch is to place it under a directory called branches in your repository. In the "To URL:" portion of TortoiseSVN's Branch dialog, you would therefore enter something like:

(svn/http)://path-to-repo/branches/your-branch-name

The main branch of a project is referred to as the trunk, and is usually located in:

(svn/http)://path-to-repo/trunk

In the Repository Browser of TortoiseSVN, find the branch that you want to create the new branch from. Right-click, Copy To.... and enter the new branch path. Now you can "switch" your local WC to that branch.