How to transfer my sim from iPhone 4 to 4s?

I have the iPhone 4 and just got the 4s. My mum is having my old iPhone and so she's sorting out a micro sim… But when I put my sim into my new phone will all my apps and contacts and pictures etc.carry over?

Yes all contacts will.apps pics etc are stored on a micro sd if that is what you mean then yes they will appear wherever you insert the mico sd card

Nope. Apps aren't stored on the sim. You need to back up the old iPhone to your computer, transfer the old sim to the new phone and restore the new phone using the backup from the old one. That will copy everything over.
You can keep the apps and everything going on the old phone and use it as an iPod if you want. You just have to put the sim card back in to update them. The sim is what identifies the phone to iTunes.