Cost to restore my iphone?

"Restore" may have many meanings:

• Erase information and settings and install latest iOS version: This costs nothing as VioletRA and paulcb suggest.
• "Restore" as in "my iPhone has significant hardware damage and no longer functions. I need it restored to a working condition." In that case, you will likely have to pay for a hardware repair. Visit an Apple Store or Authorized Apple Service Center, let them inspect the iPhone, and advise you.

Do they charge you to restore your phone

Can apple restore my phone because my internet is not working

LOL nothing

You can download iTunes from the Apple Support Site from right above in the dark gray bar

Connect your iPhone to the cumpter with the usb cord and iTunes should automatically pop up

If you see your device in the upper right corner, click on it

A summary pane should pop up

You should see a button in the iTunes windows to "Restore iPhone"

There's no charge. See this for detailed instructions... http://support.apple.com/kb/HT1414