To encrypt an external drive, connect it to your Mac, wait until it mounts on your desktop after you turn it on, and launch Disk Utility. You’ll see a left column that lists the storage devices on your Mac. The first device is your internal drive. Your external drives should follow. Select the drive you want to encrypt. Then click on the Erase tab in the section to the right.
In the Format pop-up menu, you’ll see two new disk formats available to you, in addition to the standard Mac OS Extended (Journaled), Mac OS Extended (Case-sensitive, Journaled), MS-DOS (FAT), and ExFAT. The two new formats are Mac OS Extended (Journaled, Encrypted), and Mac OS Extended (Case-sensitive, Journaled, Encrypted).
In most cases, you should pick Mac OS Extended (Journaled, Encrypted). The other encrypted Mac format lets you give files the same names but with different letter case treatment. (For example, both files named 2011taxes.numbers and 2011Taxes.numbers can exist in the same folder.) You also need to provide a name. Click Erase.