If you are still having problems connecting to the Internet after verifying your router is working by getting on the Internet through another device and going through all of the troubleshooting steps leading to this point, the best thing to do is to make sure your router has the latest firmware installed on it.
Unfortunately, this is something that is specific to your individual router. You can either consult the manual or go to the manufacturer's website for instructions on how to update the firmware on your individual router.
If you are really stuck and have no way (or no idea) of how to update the router's firmware, or if you have already checked to make sure it is up to date and are still having problems, you can reset the entire iPad to factory default. This will erase all settings and data on the iPad and put it in a "like new" status.
You'll want to make sure you sync the iPad before performing this step so that you back up all of your data. Once you have plugged the iPad into your computer and synced it through iTunes, you can follow these steps to reset the iPad to factory default settings.