Apple's iPhone is unlike other smartphones and feature phones. Instead of having to remove the back and the battery to insert the SIM card, the iPhone features a small SIM card tray located in the top edge of the device. This must be removed using a dedicated small pin (or a bent paper clip if you can't lay your hands on the pin) for the SIM card to be inserted. Here's how to put a SIM in an iPhone.
Contained within the manual for your iPhone (3G and above) is a small pin designed for use in removing the SIM. However, if you're not in possession of this, a bent paper clip will do the same job. Insert this in the tiny whole located on the top edge of the handset to remove the SIM tray.
Insert the SIM, contact side down into the tray and then push it back into the handset. Now switch the phone on and wait for it to boot-up.