If you are on Windows then the best client I've found so far is http://tortoisesvn.net/ with that you can browse the repository from the right click content menu in explorer and delete the folder directly from the repository. Once you update the working copy the folder should be removed form the working copy.

You can also operate on the working copy and check it back in, again the right context menu in explorer gives you access to tortoisesvn functions e.g. delete.
If you have your common code in a repository e.g. http://subversion.example.com/svn/proj/trunk/files and you want that folder to appear in a different projects libs folder then if the target project has the structure:

trunk/src/system/libs/

You can add an svn:externals property to src which would be:

svn:externals system/libs http://subversion.example.com/svn/proj/trunk/files

Now when you checkout/update the target project it will automatically pull files from the external repository.

Paths need to change to match your environment and I really recommend creating a set of test repositories to play with.

The book I like for Subversion is Pragmatic Version Control Using Subversion (http://www.compman.co.uk/scripts/browse.asp?ref=792367) I actually thought it was 3rd Edition now, but that covers externals on page 142

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