For example if I were configuring my PC to browse the web over HTTP and I have denied all inbound and outbound requests and responses, would I need to only open port 80 to outbound requests or would I need to open port 80 to outbound and inbound requests?
Your question is a bit on the vague side. There are many different firewall implementations.
On old low-end firewalls (stateless packet filters) you had to write rules to permit or deny the traffic for both directions. Most firewalls these days are stateful. If you build your rules the correct way, then you can write a rule to permit the connection to be established, and once it is established everything else will be permitted. You can still write stateless rules on most stateful firewalls.
A linux iptables based firewall would setup stateful connections like this. Note I am only have an explicit rule for the incoming connections to the mysql server, the outgoing will be handled by the ESTABLISHED rule.
If the firewall you curious about is not Linux based, you will almost certainly have to dig into the docs for that specific firewall.