First, go to your home screen, make sure you are within Bluetooth and Wi-Fi range of the other device (also make sure both of these features are on), and make sure neither device has a personal hotspot on.
If one or both of them do, turn off the personal hotspot.
Open the app that has the data you would like to transfer. In my case, I am transferring a photo, but there are several data types you can transfer including most file types.
Find the specific data, in my case the photos, that you want to send via AirDrop and select it.
Click the share button at the bottom of the screen.
Click the AirDrop button.
On the recieving device click "accept." You'll notice on the original device it will say "waiting."
Once you click "accept" the data will then begin to send, and can take anywhere from a few seconds to a few minutes depending on various factors like file size and internet speeds.
That's it! The data is sent and you just AirDropped some data!