If the new server contains the stuff you want to use completely, meaning that there isn't anything in the old working directory that you need to commit, the best method is to rename the old top level directory to something like website-old, and then do a fresh virgin checkout of the new svn repo.
It is possible to change where your checkout points to if you need to commit something. For this one uses the relocate command, as such:
svn relocate svn+ssh://new-svn-server/path/to/repo/trunk/