You won't find an answer to your question, sadly. That's just because there aren't many solutions to what you're looking for because there aren't many reasons to have it on Linux.
There are some options that I can think of:
1. Uninstall the application that is connecting to the internet when you don't want it to.
2. If you know the hostname(s) of where this application is trying to connect, enter those hostnames as 127.0.0.1 in your /etc/hosts
3. Enable SELinux and change the policy for the said application(s).
4. Use iptables to block connections on the protocol it is using (not a good idea if it is http or any other needed protocol) in a rule based on the user running the process. OR use netstat to find the ips your unwanted connections are going and block any outgoing connections to those IPs.
5. Grab the source for the 'offending' software and patch it
6. As lysharia mentioned, if you are using a control panel there may be some settings to do that sort of thing. I don't know of any control panels that do this, but it is possible.
6. Disconnect from the internet altogether.
But you won't have much luck in finding many people who know how to install any firewalls with application based rules because there really aren't any.