Yes you do - you need to contact your phone company and get them to activate your new sim (to essentially switch your phone number from the old sim to the new one)
Despite my 'they just work' post of earlier, this was the one hiccup I ran into with mine as this wasn't explaiined anywhere and I only discovered it by googling.
Boom! Thanks Dr Marbles.
Last question (probably)
So now I can make phonecalls.. Hurrah!
But when I switched the wifi off, the iphone won't get onto the internet.
Help appreciated.
What network are you on?
For my mum's phone who's on giffgaff I had to go through this procedure to sort the same problem:
STOLEN FROM GIFFGAFF website......
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From your iPhone home screen, click on the icon "Settings" > click "General" > click "Network" > click "Mobile Data Network" > tap on the words next to "APN" and you'll then be able to edit the settings
APN - giffgaff.com
Username - vertigo
Password - password (This is the word "password" not your giffgaff password)
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Her APN was set to O2.com so I just changed it and it was job done.
If yours doesn't look similar to whatever network you're with then I'd guess you need to find out what it needs to be and change it as well.
Good luck.