According to Apple iPhone Manual, inserting a SIM card in iPhone is pretty easy, all you need is the SIM eject tool provided by Apple. If you do not have a SIM eject tool you could also use another blunt object like a paper clip.
To Insert/Install SIM Card in iPhone 4, follow the steps given below:
Step 1: Insert the end of the paper clip or SIM eject tool into the hole on the SIM tray. Press firmly and push it straight in until the tray pops out.
Step 2: Pull out the SIM tray and place the SIM card in the tray. The angled corner of the SIM ensures that the card fits only the correct way in the tray.
Step 3: With the tray aligned, carefully replace the SIM tray containing the SIM card in iPhone.
Once you have inserted the SIM card into the device iPhone will recognize it and allow you to use the device.