[or… how I learned to stop worrying and love the /etc/group file]
On Red Hat, the default permissions for a serial port are:
ls -l /dev/ttyS1 crw-rw---- 1 root uucp
This means that root is the owner and group is uucp. No others have access to the serial port. In order for a non-root user to use the port, then, you need to add the user to the uucp group. To do this, simply edit the /etc/group file. Find the uucp entry, and add a comma and the username you want to belong to the group:
In this example, usernametohaveaccess now has access to ttyS1.