Moving an existing database from an old version?

I'm sorry if this has been answered before, but I've searched through
the archives and haven't found anything.

I have a machine that was built about two years ago and runs Debian. I
just built a new machine running Fedora and PostgreSQL 8.x. The old
machine has an older version of PostgreSQL running on it that seems to
keep data in different locations than the new one. I have found the
.conf files and they don't seem to tell me where the data lives.

What I want to do is simply transplant the existing application onto the
new database. I'd be happy to simply copy the files over and hack the
.conf files appropriately, or if it's better, can I use PG_DUMP to
somehoe backup the old data and restore it to the new installation?

I appreciate any pointers you may have or suggestions as to where else I
might look.

Or if you want to help out in exchange for lunch money, that could be
arranged too. :)

Thanks!

Howard