It's pretty straight forward. First, your DBA will backup and then
restore the databases to the new server. Be sure he gets all 4
databases: prof,serv,site, and config. Next, go into SharePoint
Portal server  Central Administration page. Go to the Configure server
topology page (it's the first option). There you will see a list of
all the databases. Just select each and change them to point to the
new DBs. I've done this many times and it seems to work fine.

I eventually succeeded, but it was not as straight forward as that...
First of all I had to modify the location of the content database server, then
the component settings DB server, and then modify the configuration DB server.
And if I wanted to do that, I had to disconnect my SPS server  from the existing
configuration DB first; and before that, I had to remove the active components
running on my SPS server (and that means reinitializing my indexes); then I had
to connect to the new config DB on the new server and restart the Web, Search
and Index components. Also, for a reason unknown to me, I had to stop/restart
IIS in order to make it work.
So, would I have a configuration problem ? According to SPS itself, "my farm  is
fine".