How do I dump one project out of an SVN repository which contains multiple projects?

You can use the svndumpfilter utility to do this. The SVN book has a good explanation of how to do this.

For instance, one way would be:

$ svnadmin dump /path/to/repo 
     | svndumpfilter include /proj > dump-file
$ svnadmin create /new/proj/repo
$ svnadmin load --ignore-uuid /new/proj/repo < dump-file
$ svn rm file:///path/to/repo/proj