I will assume that you have a wireless router that gives out IPs automatically when connecting to your network and it's protected by a password.
If that's the case, we should consider the following options:
Reset iPod's wifi settings
- On your iPod, go to Settings -> Wi-Fi
- Make sure Wi-Fi switch is set to "ON"
- In the list of wireless networks under the "Choose a Network" label, find your wifi
- If there is NO check mark on it, tap on it and enter your wifi password; if there IS a check mark tap on the arrow that's on the right side (white arrow in a blue circle), then select "Forget this Network". A confirmation popup will appear - tap on the red "Forget" button.
- All the fields like IP, Mask, etc. should now be blank; tap on the "Wi-Fi Networks" arrow that's in the top left corner of the screen
- There shouldn't be a check mark next to your wifi name anymore; tap on your wifi and enter the password; tap the Join button and in a moment you should be reconnected to your router. If all went fine, you should be able to go online right away.
Restart the wireless router
If the steps above did not help, you should restart your router.
Many routers have a small reset button, usually in the back. It takes only a second of pressing this button with something thin, like a paper clip, in order to reboot the router. Hold it longer and you might reset all configurations to default settings (I would not do that since all other devices are working fine with the current setup).
In case you can't access the reset button, simply unplug the power adapter.
Some routers carry a battery as well, you'll know if yours does if the LEDs are still on after you unplug it :) These batteries are easily removed, almost like the ones on laptops.
I would actually recommend the "unplug" method. I'm located in Florida and due to often power outages some devices not protected by a power surge might accumulate some static on boards. Leaving a device (router) unplugged for about 15 minutes is a easy workaround.