There are all kinds of reasons why you might want to format a storage drive for your Mac - from cleaning it up for a fresh install of OS X to creating an encrypted drive for work. Or even creating a Windows partition. Fortunately Disk Utility, built right into OS X, can help. And it's easy to use too. (See all of our Mac tips and Mac tutorials.)
Updated 5 July 2016 with general updates.
Format storage drive for Mac step 1: Launch Disk Utility
The first thing to do is head to Applications > Utilities, which can be found through the Finder and you'll want to open the Disk Utility application.
Once it's open you'll see the list of available drives on the left. Choose the drive you'd like to format and then click on the Erase option from the four options available in the main window.
Format storage drive for Mac step 2: Choose your format
Disk Utility automatically chooses OS X Extended (Journaled) as the default format for the drive format, but if you'd like to use something else click on the Formatting options to reveal its drop-down window. In our case we used a USB to demonstrate the formatting options.
The other options you'll now see are:
OS X Extended (Journaled) - useful for creating secure drives that require a password to access. Encrypting laptop and external drives is a great idea if you're always lugging your laptop around and don't want anyone to access the contents of the drive should you accidentally lose it. Ditto for removable drives like external drives and USB keys.
Mac OS Extended (Case-Sensitive, Journaled) - by default OS X treats lower-case and upper-case files on a drive the same; but if that's an issue for you, you can create a case-sensitive drive where they are treated differently. So a file named Macworld.txt and macworld.txt would be treated as two separate files. While this can be an option for some people, it's not recommended. (See also: How to test ping on your Mac.)
MS-DOS (FAT) - you might want to use this if you regularly share drives with PC-owning friends or colleagues and want them to be able to access the files you place on the drive on their computers. Or to create a Bootcamp partition so you can install Windows on your Mac.
ExFAT - the same as for MS DOS (FAT) above, only this option has been optimised for flash drives - both internal and external.
Format storage drive for Mac step 3: Name your drive
Once you've chosen the drive format you want to use, you'll now need to give the drive a name. This can be anything you like, but choose something obvious like 'Macintosh HD' if you're going to use the drive as your Mac's main drive or 'Bob's Mac' or 'Videos' if you're using the drive to store videos, etc. (See also: How to run Windows on a Mac.)
Format storage drive for Mac step 4: Choose a security option
Click the Security Options button towards the bottom of the main window. This will bring up another window that enables you to choose how you'd like the drive to be formatted, with a slider ranging from Fastest to Most Secure.
Fastest will erase the drive by removing the header information, but will leave the underlying files intact, although they will be hidden. This means you or someone else could resurrect the files easily using data-recovery software, which isn't necessarily a good idea. For a fresh install of OS X, we'd recommend you move the slider to the second option where it says "This option writes a single pass of zeros over the entire disk." This will overwrite the entire drive once.
For higher security, continue moving to the slider to the right. The next step will give you the option to overwrite the drive three times. Moving it the entire way to Most Secure will overwrite the drive seven times - but you'll have to wait quite a while (depending on the size of the drive) before it will be available for you to use again.
Format storage drive for Mac step 5: Format the drive or USB
It's finally time to click the Erase button. Now go and do something else, like gardening, or a puzzle. Or spend some time with your friends and family. Formatting a drive can take a while, especially if it's large and/or you've chosen one of the most exacting Security Options. A progress bar will show how the formatting of your drive is going and how long, roughly, it will take to complete.
After a little while your formatted drive will finally be ready for you to add new files to. Tremendous stuff this technology, isn't it? (See also: How to take a screenshot on a Mac.)