This is not a tutorial for finding already-known and indexed old sites. This page will give you some tips on finding websites that may have not been looked at for 20+ years. I would advise you to submit the pages you discover to Wiby to help the internet become more useful and exciting.

The Geocities Gallery is run by the restorativland project and is an excellent way to find old websites that have been saved before Yahoo closed Geocities in 2009. It is different than the Wayback Machine because there aren't multiple snapshots. There is simply only the latest archive of the page available.

Alexandria search can be a good way of finding more recent obscure sites. It also works without Javascript.

You can use dorking commands on Google and DDG to search for specific web hosts and filter by dates. For example you can type site:web.fc2.com to find a bunch of ancient Japanese sites. I do this straight after I find a new webhost. You can pair this with a search query: site:web.fc2.com 初音ミク to find old websites about Hatsune Miku. If you want to search for all FC2 sites about Hatsune Miku before 2009, you can use the before: command like this: site:web.fc2.com before:2009 初音ミク.