It's a widget, not an app. I copy/pasted from the description in Play, but it's the same procedure for all widgets:
STEPS HOW TO ADD A WIDGET
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1.On your Android home screen, tap any blank or “empty” area with size 4x2 and hold down your finger.
2.An “Add to Home screen” window will pop up. From that window, tap “Widgets”.
3.You’ll be presented with a list of all the installed Widgets on your Android device.
4.Select the "Rings Digital Weather Clock” to add to your home screen by tapping it.
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After it's on the homescreen you can tap it to get more information and get into settings etc.
Edit:
Oh and. To remove the thumbnail, long press it and slide it up (I think, don't use the stock launcher) to the X or trashcan, then release. It's not going to delete it, just takes it off the screen.
You can also move things (widgets included) around the same way, just drop them where you want instead of the trash
Oh and and, welcome to the forums!