Keep these simple troubleshooting tips up your sleeve for the next time you have problems connecting your iOS device to a Wi-Fi network. Here are some basic steps borrowed from a short article in Macworld.
The first thing to try is the most simple and obvious: turn your devices off and then on again. Restart your iPad or iPhone by holding down the power button, and restart your Wi-Fi router by unplugging it and then plugging it back in after about a minute. If no luck, then go to Preferences>Wi-Fi and turn the Wi-Fi switch off and then on. If that doesn't work, then back in Preferences>Wi-Fi tap the blue dot and then "Forget this network." Then select your network again and log in. The next thing to try would be to go to Preferences>General>Reset>Reset Network Settings. After your device reboots, then again select your network in Preferences>Wi-Fi and enter your password.
This should fix most problems. I find that if I'm in a public area and am not in a position to turn off the public router, I can at least try restarting my iPad by holding down the power button. That alone will usually fix the problem. Also, I've found that sometimes even though my iPad shows that it's connected, but nothing is working, I simply need to log onto the network again by going to Preferences>Wi-Fi and selecting the network and then logging in.