Hi @bedath and welcome on here
The SIM can take up to 24hrs to activate, although it is generally faster. Your new phone number shows up on your dashboard when you log in to "My Giffgaff" this means your SIM has been activated.
It will help to re-start your phone a few times during the day whilst the activation process is going through.
You can acess from your phone
Text NUMBER to 2020 and you will receive a text back with your giffgaff mobile number
or whilst on here Hover over your Username Top right and choose My Profile and Settings and it will be there.
Also other important GiffGaff numbers should have been added to your Contacts list on the phone.