Where rock has the backbeat, jazz has the ride pattern: a four-beat phrase on the ride cymbal that goes "ding · ding-a · ding · ding-a" — quarter, two swung 8ths, quarter, two swung 8ths. The 8ths are swung (the second of each pair plays late, like the third note of a triplet). This is the heartbeat of every jazz groove.
Build it the same way you'd build any complex coordination skill: top-down. Quarters first. Add the skip-note. Add the hi-hat foot on 2 and 4. Add the bass drum on 1. Each layer is a new limb that has to know its job.
Getting the Swing Right
At medium tempos the skip-note lands like the third note of a triplet: "ding-a" is a triplet with the middle note missing. Two failures sit on either side of it. Play the 8ths straight (50/50) and it stops being jazz; swing them too hard and it turns into a stiff shuffle. The ratio also breathes with tempo: swing tightens toward even 8ths as things get fast, so trust your ear over any formula.
The ear is trained by listening, and there's no substitute: put on a classic ride-driven record and play along until your "ding-a" disappears into the drummer's. Keep the skip-note lighter than the quarters; it decorates the pulse, it doesn't compete with it. And check the hi-hat foot — eager left feet love to sneak ahead of 2 and 4.