You link your webpage to the core jQuery library.
Then you tweak the settings offered by the plugin to create the effect you want.
Then you upload your complete webpage (including the jQuery and plugin components) to the web.
The core libraries are stored on Google API, Microsoft and jQuery.
You don't need to download the library. Just reference one in your HTML code between the <head> tags.
Some older plug-ins may not work well with the latest jQuery release. In that case, find a newer plug-in or drop back to an earlier library.
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You can either download it and host it on your server (but it does get updated) and there's no real need. Or, better, link to it on public servers
Note: there are other JS frameworks out there too