The activation usually takes about 30 minutes, but Giffgaff say 'up to 24 hours'. When the SIM is activated you will see 'Giffgaff' in the top left hand corner of your phones screen. I'm adding tis info. to help you through the process.
***ACTIVATING SIM: When activated your new phone number will be shown***
Follow the instructions on the card attached to the new SIM & wait up to 24 hours (usually 30 minutes).
Switch the phone on & off a couple of times.
When activated you should see Giffgaff in the top left-hand corner of your phones screen.
If you still have a problem look at the following link:https://support2.giffgaff.com/app/ask/Getting-Started/Activating-my-SIM/form/
For any other queries:
ASK AN AGENT: https://support2.giffgaff.com/app/ask/
“My Giffgaff” page here http://www.giffgaff.com/dashboard