How do I configure PostFix to allow other machines to send out email through it?
You will need to configure relay. However when postfix is running you should be able to still connect to port 25. Might there be a firewall blocking this connection?
When you open main.cf, you can need to add this directive:
mynetworks=A.B.C.D
example:
mynetworks = 127.0.0.0/8 168.100.189.0/28
mynetworks = !192.168.0.1, 192.168.0.0/28
mynetworks = 127.0.0.0/8 168.100.189.0/28 [::1]/128 [2001:240:587::]/64
do not put 0.0.0.0 or you will become an open relay.