Launch iTunes from your list of applications.
Connect your iPhone to the computer via USB and select it from the toolbar. If you are still using an old version of iTunes you can select your device from the sidebar.
Before continuing click the Back Up Now button from the Summary tab to ensure your device is backed up before the update.
Click the Check for Updates button to see if there are any available updates. If iTunes has already detected an update click the Update button.
iTunes will inform you if an update for your device has been found. Click the Update button to continue.
Read the update's changelog and click Next.
Click Agree to agree to Apple's Software License Agreement.
iTunes will begin downloading the new firmware. This may take a while.
Once downloaded, the firmware will be extracted and installation will begin.
iTunes will inform you once the installation is complete and your iPhone will reboot.
You may be informed that there is a carrier update for your iPhone. If there is, click the Download and Update button. The settings will be updated. Click OK to acknowledge the successful installation.
That's it! You've successfully updated your iPhone to the latest firmware version.
If you need any help with these steps please ask a question here.