If you have a TeX distribution such as MacTeX, TeX Live, or MiKTeX installed, you may simply open it at the command line by thhe command “texdoc asymptote”.
You can read it online for the current TeX Live version at the TeXdoc site: texdoc.org/pkg/asymptote.
At the homepage asymptote.sourceforge.io, you find the most recent documentation, and a gallery with many examples and their source code.
Here’s a brief look at the 2D examples:
And here’s a look into the 3D example gallery:
Very recommendable!
There’s also a list of Frequently Asked Questions.