If you've got a new iPhone with a pay monthly 4G-ready SIM, you'll need to connect your iPhone to iTunes or WiFi.
If you've connected to iTunes, you should then see a Window that asks you to install carrier update settings. Click 'Update settings' now, which will begin the update and before you know it, you'll be able to connect to speedy 4G internet.
If you connected via WiFi, you can go to Settings > General > About, and then tap 'Update' to update your carrier settings.
It's worth noting that not all areas support O2's 4G yet. To find out whether your area has 4G coverage, you can use O2's tool here. If you're struggling to update your carrier settings and connect to 4G, you can also use O2's 4G setup wizard here.