My Passport external backup

Plug in the external hard drive. Launch Disk Utility (Applications folder > Utilities) and highlight the top entry of the external drive in the left column. Go to "erase"and choose what it shows in my screenshot - also name it whatever you like such as "iMac backup". When done, you should see an icon for it on your desktop.

You are all set to launch Time machine.

Any external drive is fine; make sure you format it for Mac first and erase whatever software is on it - no external drive needs any software to function. Once erased and formatted, turn on Time machine and you are good to go.