There are only few simple steps to migrate svn repository from one server to another. In this post I describe them.
As I told in several other posts, we had severe problem with electricity outages in Barcelona. As a busy phd student with a need for a usable remote server, that's no option. In my post on commercial remote backup servers I discussed alternatives. I am moving my subversion repositories to the new server now.
First step: copy your remote repository from oldserver to newserver. This can be done in different ways. Simplest is using rsync, scp, or others (optionally involving dump files).
Second step: (on client)
svn switch --relocate oldurl newurl
See also my posts on basic subversion commands and automated backup using subversion.