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the S3 uses a microSIM instead of the normal size SIM. Quickst way to get hold of one is to nip into your local Vodafone store and they can swap it over for you free of charge.
Just to Add to Nabs' great advice...
The Store will provision the New Micro Sim with your details. This process takes minutes in Store and then approx' 30min to activate on your account. During this time your phone will be off.
It's also a good opportunity to use the "RedBox" service to transfer contacts etc. from one phone to another.