Literally: find a favorite (not dead) author’s website and use their contact form to send them a message with specifics about why you like them.

I’ve done this several times. The nice thing is they’re usually very accessible and responsive, maybe because they tend not to get the same kind of public praise as actors, musicians, and other more glamorous artists.

Of course this does depend on the author’s level of fame. My favorites tend to be nonfiction writers with an approachable-enough profile to still be accessible by civilians, so if your favorite author is a Cormac McCarthy type then you’re SOL.

You can do this over social media, but a mere “Love your work!” doesn’t have the same effect as a more detailed note, which both proves you’re actually a fan and gives them the fuel to keep going and making more stuff you enjoy.

Anyway, try it sometime.