Update To iOS 7 Over-The-Air (OTA)
Step 1) - Launch the Settings app on your iPhone, iPod Touch or iPad, go into the General tab and then the Software Update tab.
Step 2) - You should now see a screen stating that the iOS 7 firmware is available to install on your device. Tap the Download and Install button.

Step 3) - Accept the Terms and Conditions and then the iOS 7 firmware will begin downloading. You should also be prompt to plug your device into your computer to ensure there is enough battery to complete the download and finish the installation process.
Step 4) - While the iOS 7 firmware is downloading you can exit out of the Settings app and continue to use your device. When the firmware has finished downloading you will be prompt to install the update. Tap the Now button and the iOS 7 firmware will be installed to your iPhone, iPod Touch or iPad.

Update To iOS 7 Through iTunes

Step 1) - The first thing you will need to do is download the official iOS 7 firmware for your iPhone, iPod Touch or iPad.
Alternatively your specific firmware version can be downloaded from iTunes once you plug your iOS device into your computer upon clicking the Check for Updates button. If you do this then you do not need to follow steps 2 and 3, simply follow the on-screen instructions.
Step 2) - Once you download the iOS 7 firmware for your iPhone, iPod Touch or iPad you will need to connect your iOS device to your computer. When iTunes launches you will need to click on your iOS device from iTunes side navigation.

Step 3) - After clicking on your iOS device you will simply need to SHIFT click the Check for Updates button (WINDOWS) or ALT click the Check for Updates button (MAC OS X). Of course if you would like to do a clean install of iOS 7 you can click the Restore button instead (those currently Jailbroken will need to perform a restore rather than an update).

A new window will now appear where you will need to select the official iOS 7 firmware file you downloaded earlier. Select the firmware file now and your iPhone, iPod Touch or iPad will begin being updated.
DO NOT touch your device during the restore process and DO NOT use your computer. After approximately 5 – 10 minutes it will reboot into a usable state. Congratulations you are now running the official iOS 7 firmware.