In iPhone 3G, it was very easy to remove SIM card by using a pin in the top part of the SIM tray. However, in iPhone 4 the location of SIM has changed. Also, iPhone 4 uses Micro SIM card and not the normal SIM card.
Earlier I posted a tutorial on inserting a new SIM card to iPhone 4. Here’s video tutorial for the same. It shows how to remove the existing SIM from iPhone 4 and then how to insert a new one. Check it out!