I accidentally bought a mister handy instead of a lunchbox. Now that I have him, I can't see how to actually put him in the game and use him. He's not in the 'dwellers' menu in the upper left, nor in the 'settings' menu in the lower right. It seems like it should be obvious, but I don't see anything.
First things first, you need to free Mr. Handy from his shipping box. If you go to the "open a lunchbox" screen, you should see a sort button near the bottom. Tap that to switch between Mr. Handy boxes and regular lunchboxes. After a Mr. Handy box is at the top of the queue, tap in the open lunchbox area to unpack him. He should float onscreen and wait in line at the entrance to your vault.
After Mr. Handy is in line, drag and drop him to the floor you want him to work on. He will float around the rooms on the floor, collecting from full resource rooms and assisting during any incidents (fires/radroaches/etc).
You can only have one Mr. Handy on a given floor, but you can drag him to other available floors as you like. Mr. Handy doesn't take up a dweller slot, and he won't show up in the dweller list when you tap the gear icon.
For more information about everything Mr. Handy can do.