In the end, this guide ended up way longer than I was expecting, but I hope you'll find it useful, although it often replicates information already available in pkgdown documentation !
Prerequisites
To build a website using pkgdown, all you need to have is an R package hosted on Git Hub, with a file structure "tweaked" with some functionality provided by devtools.
Assuming you are using RStudio, and that you didn't already do this, open the project corresponding to your package and (as a minimum) run:
require(devtools)
use_readme_rmd()
use_news_md()
use_vignette("test") #substitute with the name of your package