Inline the CSS needed to render above-the-fold content; load the rest asynchronously. The savings on slow networks are real — first paint happens on the first round trip.
For dynamic pages, automate extraction with Critters, Penthouse, or Beasties (the Critters fork). For mostly-static pages, hand-inline once and re-run when the design changes.
Pair with <link rel="preload" as="style"> for the deferred sheet so the browser fetches it ahead of time.