Can I use my computer's network connection on my Ipod?
Not exactly but you can use the computer's ethernet internet connection via Wifi to the iPhone.

In that case just go to System Preferences > Sharing, then


Select Internet Sharing
Select Ethernet in the field Share your connection from
Flag Wi-Fi in the field To computers using
Go to Wi-Fi Options... and select a network SSID and a security password
Click OK
Flag Internet sharing


If you are using a pc with windows you can follow the instructions reported here. Basically:


Go to Network Connections in your Control Panel by going to Start > Control Panel > Network and Internet > Network and Sharing Center and then click Change adapter settings on the menu on the left.
Right-click your Internet connection that you want to share (e.g., Local Area Connection) and click Properties.
Click the Sharing tab.
Check the "Allow other network users to connect through this computer's Internet connection" option.