Does it cost any money to use the internet on an iPod Touch?

Not at all, although, you must have an internet connection at home (with wireless router). You can also use the internet if you're in range of a wi-fi connection or hotspot (e.g. local library, Starbucks, Coffee Bean).
Does it cost any money to use the internet on an iPod Touch?
no it doesn'tt, as long as you have internet service in you house or where ever your using it at...