To build a module by hand on a Unix machine,* is this correct?

I put the unpacked source into /home/user/.cpan/build

That doesn't matter. You can build and install it from any directory.

Navigate to that directory and type

perl Makefile.PL
make
make test

make install

You probably need to be root for this step.

And this creates the proper (everything)?

Yes

And -- when removing modules on a Unix machine, I just remove the same directory that was created in /home/user/.cpan/build -- is that correct?

No. The "make install" installs the module into your library path (probably under /usr/lib/perl5/5.8.x/site_perl). You'll need to manually remove the files from there.

What about one other thing -- is there a central file or database that keeps track of all installed modules? Do I have to remove an entry from that?

Try "perldoc perllocal" for this list.

One node here says that using CPAN and 'clean' will remove a module as well. Can someone verify that...

That's nonsense. That will just clean up the directory that you ran the installation from.