If your wireless keyboard is still connected to your iPad, or if another wireless keyboard has paired with your iPad, you may find that your software keyboard does not show up when expected. Tapping the eject key on the wireless keyboard should solve the issue. If not, try these steps.
Generally, when performing actions such as tapping on a text-entry field in a Web page, tapping on the URL-entry area in Safari, or typing in Notes or Mail, your software keyboard should show up if no wireless keyboards are paired and active with your iPad.
If it does not appear, and ejecting your wireless keyboard does not allow the software keyboard to appear, try unpairing the device by navigating to Settings > General > Bluetooth > Forget this Device. You might also try powering down the wireless keyboard that is causing the interference. If neither of these solutions work, try disabling Bluetooth by navigating to Setting > General > Network > Bluetooth.
You can also try resetting your iPad (hold the Home button and Sleep button at the same time until you see the Apple icon appear).