If the update is for an app, initiate the App Store app, select the "Updates" option in the bottom right corner of the screen, and then select to update the app. If the update is to iOS, go to Settings → General → Software Update and select to update to the listed iOS version.
Try toggling wifi off, then back on. Then do a hard reset.
Hold the top or side power/sleep button and the home button at the same time until the Apple logo appears, then release.
Then do Reset Network Settings.
Reset Network Settings Settings>General>Reset>Tap Reset Network Settings. You may need to enter your wifi passcode back in afterwards.