Downloaded Skype but no icon appeared on iPad. App store says installed.
What am I doing wrong

Sometimes, you may have too many icons loaded for the iPad to display. So you'll either need to remove some apps or put some into a folder.

Or, it may have installed to a different page if your second page is full. Check the other pages...

If neither of those two are the case, then do with restart or a reset of your iPad (or both). To do:

Restart: Hold down the power button until the power off slider appears. Slide it off. When the iPad finishes shutting down, hold down the power button again until the Apple logo appears.

Reset: Hold both the power and home buttons until the screen goes dark and the Apple logo then appears (the slide to unlock screen may or may not appear). Once the logo appears, release the buttons. After a time, your homescreen will appear. Please note that it may take some time for the Apple logo to appear or for your homescreen to appear (or both). This is normal. Eventually, the homescreen will appear.

Hopefully, you will find that pesky Skype app. Good luck and let us know how you get on.

Marilyn