Set the setuid bit on the executable
$ sudo chmod u+s /usr/bin/screen
$ ls -l /usr/bin/screen
-rwsr-xr-x 1 root screen 360952 Jan 18 2038 /usr/bin/screen
Update your .screenrc
multiuser on
acladd bgates,lellison,gvanrossum,dknuth,dnorman
User 1 starts a screen session
user1@localhost $ screen
User 2 connects to the screen
user1@localhost $ screen -r user1/