how do you set up an external hard drive?

For TimeMachine? or for data, would be basically the same.

1. Open Disk Utility (located in the Utilities folder).
2. Connect the disk if it isn't already attached.
3. In the left side of the Disk Utility window, select the disk you want to use with Time Machine.
4. Optional: If you want to partition the disk, click the Partition tab and select a layout. Make sure "Mac OS Extended (Journaled)" is selected in the Format menu for the partition that will be used for backups. Click Apply.
5. Click the Erase tab.
6. Optional: If you want to securely erase the disk, click Security Options to configure, then click OK.
7. Click Erase.

http://support.apple.com/kb/HT1427 - TimeMachine Basics

The choice for an external drive, USB3 or not, the type of drive in the enclosure, probably the brand or make of the external drive (Western Digital, OWC, Seagate) is the most important choice and lot of options.

Format it for Mac OSX

Never install the "helpful" software some HD are bundled with ....EVER, its always a mistake a mess waiting to happen

Dont buy WD external HD

Never think ANY backup is safe. Always have 2 copies of data you DONT DARE LOSE. Always.

The computer itself does not count as one of those copies. 😊

Put your valuable data on it by either TM as a backup, or archive it (2nd hard drive) with your valuable data by simply dragging and dropping data onto same