If you've got an account, this is easy: head on down to this page in your preferences, set the Skin to Vector legacy (2010), and click Save at the bottom of the page. (Editing to add this: if you have an account, it will also remember whether you have the sidebar open and whether you've clicked the little button in the bottom right which reduces the amount of whitespace across pages.)

If you don't have an account or you want it to work when you're not signed in, it's a little more fiddly. Wikipedia's information page on the skins says:

If you are not logged in, you can only use the default skin (Vector Legacy), however, any user may change the skin of a page only, but only one each time, by typing ?useskin=skinname to the end of the URL (e.g., ?useskin=vector or ?useskin=vector-2022).

Only one at a time? We can do better. With the Redirector browser extension, you can automatically redirect every Wikipedia page to the old Vector theme. Just install the extension and add these two redirects:

Or instead of typing them in manually from that screenshot, import this json file with the button at the top to install them. Now, I woke up about five minutes ago so I can't guarantee that these regexes are actually correct. Seems to work though!