Been given an iPhone 4
Currently have bog standard phone with standard SIM card
Can you cut the card or is a new card required?
iPhone 4 uses a micro sim - same chip, different sized cardboard.
You can cut it
You can, though the micro SIM is slightly thinner also. (EDIT: the nano is thinner, the micro is the same I think.)
Anyway. Just bother your provider, they'll send you a new one (probably) for free.
Apparently you can cut them down yourself. I went to the local phone fix shop who did it for free, well the price of a FB 'like'
Just cut it down, you dont even have to be that accurate - print out a template if you need to and cut away
A lot of newer sims are marked or even have a push out feature, might be worth looking.
Just go to a branch of your network and ask for a new SIM for an iP4, they'll just give you a new one to fit.