Summarize:

You'll generally want to buy an external hard drive that both has enough space for you and comes from a reliable manufacturer such as Western Digital or Seagate.  Make sure that your selected hard drive has a Thunderbolt connector (also known as USB-C) since modern Macs don't support USB 3.0 connectors. When buying an external hard drive, it's often not much more expensive to buy a terabyte (TB) hard drive rather than a 500 gigabyte (GB) one. A one-terabyte hard drive will usually run under $100. Plug the external hard drive's Thunderbolt cable into one of your Mac's USB-C ports. If you bought an external hard drive that has a USB 3.0 connector, you can buy a USB 3.0 to Thunderbolt 4 (or USB-C) adapter. It's in the menu bar at the top of your Mac's screen. A drop-down menu will appear. If you don't see Go here, click the desktop or open the Finder application to prompt it to appear. It's in the Go drop-down menu. The Utilities folder will open. Double-click the Disk Utility app icon, which resembles a hard drive with a stethoscope on it. Click the name of your external hard drive on the left side of the window. The external hard drive's name will usually contain the name of the manufacturer or the model of hard drive. It's a tab near the top of the Disk Utility window. A pop-up window will appear. Click the "Format" drop-down box near the top of the window, then click Mac OS Extended (Journaled) in the resulting drop-down menu. If you plan on using the external hard drive with other non-Mac computers, select ExFAT here instead. It's at the bottom of the window. Doing so confirms your decision and prompts your Mac to begin formatting your hard drive. Once the formatting completes, you'll be able to use the external hard drive like any other storage space.
Buy an external hard drive. Attach the external hard drive to your computer. Click the Go menu item. Click Utilities. Open Disk Utility. Select your external hard drive. Click Erase. Select a format. Click Erase. Click Erase when prompted.