Selective authentication?

I'm setting up PostgreSQL for a small academic lab, where I work. The
host OS is Linux (Debian). I want to allow most users to connect to
the database without having to supply a password, but I want to have a
special user, called dbadmin, with superuser privileges. The idea is
that I (or whoever gets entrusted with this responsibility) would
connect as dbadmin *only* when the task at hand required superuser
privileges.

I'd be very grateful if someone could explain to me how to set this
up.

(If there were a simple way to obviate the need to type in a password
every time (e.g. through a suitable command in a configuration file,
such as one can do with ${HOME}/.my.cnf), then I could just require a
password from everyone, but I have not found out how to do this in
PostgreSQL.)

Many thanks in advance!

kj