Allow access to specific user only
You will have to edit your pg_hba.conf file.  If you really want to reduce possible access to a single user (see the note below), you will need the following lines, and only these:

# TYPE  DATABASE  USER       ADDRESS   METHOD
host    all       dbowner    all       md5
local   all       dbowner              md5


This means that only dbowner will have access to any DB, logging in via the Unix socket or a TCP connection (from all addresses, including localhost).  You can replace 'all' with your DB name if you want to limit access to a single DB.

After having edited the file, you will have to reload the config - depending on your system, do a pg_ctl reload or kill -HUP &lt;postmaster_pid&gt;, or do this form inside the DB, by calling

SELECT pg_reload_conf();


Please note that in the future you might want to do certain things that need rights dbowner may not have (be it SUPERUSER, CREATEUSER or something else).  Depending on the policy you follow, you'll have to edit the file again to allow further access to a user (eg. postgres) that has the necessary privileges, or you have to assign these to dbowner before closing the door on other users.