Serial internet connection, HTTP GET request

How would I go about establishing a HTTP GET request over serial? There are plenty of examples online for ethernet shields, but I am looking to do it over serial as the Uno is connected to my computer.

Any guidance/example is greatly appreciated.

You will need some sort of intermediary program running on the computer and listening to the serial commands from the Arduino.

The Arduino Playground - InterfacingWithSoftware page lists a few ready to go programs that might do what you need or it lists a number of examples using various programming languages if you need to write a custom application.