Clave is 2:3 Son, which is actually being played by on one of the musicians. You can play this as a rim click on the snare drum with your left hand:
And there is a standard cascara rhythm being played on the shell of a timbale, as well. Play this with your right hand on the rim or shell of the floor tom, or on a cowbell, or on the bell of a cymbal:
I should write up a new page of stuff for working on this style, but for now you can experiment with adding the various left hand parts from my Reed generic Latin method, and pull some bass drum rhythms from the recent page of Mozambique. There is also an old page of LH coordination parts to go with that cascara rhythm— they are pure coordination exercises, and not necessarily stylistically correct.
A couple of notes on the track: There's a little hiccup in the parts at the seam in the loop, but the time is basically steady, and you won't really notice it when you're playing along with it. The time breathes slightly, but I don't think that's a bad thing— you do have to listen and adjust a bit.
You'll notice they've borrowed a Guaguanco-type melody, played on the congas, and that it's oriented so its rhythm lines up with the 3 side of clave. Which, to my understanding, is not traditionally correct if you're actually playing Guaguanco. I went into this a little more thoroughly before; the point is, don't get too attached to hearing that melody on the 3 side.