They are many places place firewalls, what are the most important places to set up a firewall. I know that its really important to set up a firewall at the router that leads the traffic from the outside into the private network, should we add some more firewalls in the private network or is it enough with one?
External firewall like you mentioned is a must. If you have internet facing services such as website that you host from within your company servers or a DNS server etc then you create a DMZ. Which means there is a firewall between Internet connection and your Internet facing servers and then another firewall to protect your internal network.
Also you should ideally enable host based firewalls like the windows firewall as security threats are not only external but internal as well.