Below are instructions for encrypting an external drive in OS X 10.11 and above. Note that these steps will WIPE THE DRIVE so make sure there is no important data on your drive.
1. If your drive is new/blank start here (if not, skip to 2.):
Plug in your drive and when you see the prompt below click Initialize
Open Disk Utility (Applications/Utilities/Disk Utility)
Click on your external drive
If the Partition option is grayed out click Erase, if not skip down to 2.
Click Erase
Note: This will erase all the contents on your drive
When you see the Time Machine prompt click Don't Use
Back in Disk Utility click Done
2. If your drive is not new/the partition icon is NOT grayed out start here:
Make sure your external drive is highlighted on the left and click Partition
Note: If you followed the steps above and the Partition icon is still grayed out, just click on another drive then click back on your external drive
Click the Format dropdown and choose OS X Extended (Journaled, Encrypted)
Enter a Password twice and a Password Hint
Click Choose
If desired adjust the name of the drive in the Partition window
Click Apply