Well, when upgrading your server, you should:
* create a dump of the whole repository ($svnadmin dump /path/to/repo > repo.dmp)
* upgrade the server
* load the dump again into a new repository
$ svnadmin create /path/to/repo
$ svnadmin load /path/to/repo --force-uuid < repo.dmp
As for updating svn clients like TSVN:
just install the new version. Then either check out fresh working copies (I would recommend that, since you'll get clean working copies). Or upgrade the old working copies to the new format. In TSVN, you can right-click on a working copy root folder and then click the context menu entry "TSVN upgrade working copy".