[kaerast]

Find the Github account with the most forks and followers. That's probably the official repository and will link to the official website. They may not use Github of course, but there are other similar methods.

Other good signs are them being linked to from cdnjs, cached-commons or microjs. If I'm looking to solve a javascript itch I'll first browse these sites to see if there is a popular tool.

Also, if you're looking for jQuery then it's because you've read about it online somewhere. Simply go back and follow the links.