Open up the Terminal utility by going to your Applications Folder --> Utilities Folder --> Terminal
Copy and paste the following text into the Terminal: defaults write com.apple.NetworkBrowser DisableAirDrop -bool YES
Hit enter
Log out of your account by going to the Apple Menu (top upper left corner of your computer) --> Log out
Log back in to your account and AirDrop will be disabled
If you do not want to fully disable AirDrop, you can make it more difficult for someone to see your computer and share files to it via AirDrop by following these steps:
In the finder, select the Go menu --> AirDrop
At the bottom, click "Allow me to be discovered by:" and select "No one"
If you need to re-enable AirDrop on a Mac:
Open up the Terminal utility by going to your Applications Folder --> Utilities Folder --> Terminal
Copy and paste the following text into the Terminal: defaults write com.apple.NetworkBrowser DisableAirDrop -bool NO
Hit enter
Log out of your account by going to the Apple Menu (top upper left corner of your computer) --> Log out
Log back in to your account and AirDrop will be disabled
The following video was not created by Technology Services, but it shows how to disable and enable AirDrop: