What kind of equipment/settings are needed to achieve that surf rock sound.

the bird bird bird, the bird is the word

Clean, thin sound.

Fender Strats will give you a decent sound, strats have that twangy thin sound, due to it having a slightly longer scale than most guitars.

Maybe a bit of delay, or some tremolo effect.

Check out bands such as, the Shadows, Dick Dale, The Sunny Boys. The shadows aren't necessarily surf band, but Hank Marvin has a great tone for that kinda thing.

bands like the ventures, the safaris, the tornados, dick dale, etc. all more or less universally used mostly single coil fender guitars like strats, teles, jaguars, jazzmasters, or mustangs with the occasional danelectro being used to come up with a pretty interesting alternative. as far as amps go i've noticed that most surf rock musicans use what seem to be old time tube amps with about as much reverb as possible (the more your guitar sounds like it was dropped down a well the better). not an expert on basses but it seems that that typical fender basses, p-bass or jazz bass, are used in surf music.

the clean, thin, lots of treble sound that somebody already mentioned is usually associated with the "surf rock sound," but the all the fun of it comes with putting your own spin on it. but yeah man, surf rock is the bees knees.

single coil into a clean tube amp with lots of headroom and reverb
treble up
bass rolled off

Pretty much this.

Have fun with that totally narly sound, dude!

And put the tone knob(s) all the way up.

Nothing beats a truly clean fender strat playing through a hot rod deville

fuck you. Rock Lobster OWNS that song!

The blond shaggy hair over the left side of the face and a group of shirtless toned young men with a tan