Wikipedia has a page that can act as a jumping-off point here, but the instructions can be hard to follow if you're not familiar with the terminology, so I wanted to help anyone who needed a jargon-free walkthrough.
To do this, you will need a 64GB flash drive or another similarly sized storage drive. You can also download this directly to your computer's hard drive if you have the room. Additionally, you will also need a stable internet connection.
Kiwix is a pretty reliable option for this task. If you want a near-complete archive, go for the download on this page subtitled "Offline version of Wikipedia in English" that's 57 GB. The download will likely take several hours, since it's a lot of data. Avoid streaming anything or playing online games while you're doing this to speed up the process. It'll download as a special filetype called ZIM.
Then, you'll want to go to the Kiwix Applications page and, depending on if you're using an Android, Windows, or iOS device, you'll download the compatible version of the reader. You can also download one of the versions that uses Chrome, Firefox, or Edge. Even though those are browsers, once you have the plugin downloaded it should work offline.
If the file downloaded as a ZIP file (this'll be the case for Windows), you will need to unzip it. Right-click the ZIP file and select "Extract All..." and select where you'd like the file to end up. The unzipped file will contain a file that ends in .exe, likely named "kiwix-desktop.exe". Open this up to get to the program. It will show you a list of online-available files that you can download, and if you already downloaded the offline Wikipedia archive ZIM, you should be able to find it in the "Local Files" section.
If you downloaded one of the browser extensions, all you need to do is open up that extension once while connected to the internet to enable it for offline use. You'll then be able to add the ZIM file or files that you have downloaded.