Demon Hunters are the new hero class coming in Legion. Fun fact: their class color is a kind of magenta-purple - lighter than Warlocks, but not a pink like Paladins. Actually, you might just call it straight purple, with Warlocks having indigo, but anyway.
Obviously, as a new class, Demon Hunters are still very much in development. So while there are the usual caveats from other spec break-downs, it goes quadruple here - this is a new class and a new spec and it's still in beta, so expect lots of changes down the line.
As this is all new, we'll start with some class basics.
Demon Hunters use a resource called Fury. I'd say it's something akin to Runic Power - you generate it via abilities and then spend it with other abilities. It looks like Fury is going to be much more easy-come, easy-go than a lot of other resources, as there are quick ways to get up to 100 and abilities that cost large amounts. You're going to see that purple bar bounce back and forth a lot, is what I'm saying.
All Demon Hunters are going to have a fantastic amount of mobility, with double-jumps and glides as additional features for the Jump button, and also a quick dash called Fel Rush that has a quick recharge.
But let's talk Havoc, the Demon Hunter DPS spec. At the moment in the Alpha, it's the only Demon Hunter spec, as they're still clearly doing a lot of internal iteration on Vengeance (the tank spec.)
Demon's Bite is your main Fury generator. It has no cooldown, does a physical melee strike, and generates 20-30% Fury. That range of fury generation is kind of the cool hook, as you'll have to react to how much Fury you actually have, without being able to do the rotation blind. This will probably be the ability you use when you can't do anything else.
Chaos Strike spends 40 Fury to do a Chaos-damage melee strike. The interesting wrinkle here is that if this ability crits, in doesn't consume any Fury. So a high-crit build might allow you to chain a bunch of these together for massive damage.
Eye Beam costs 50 Fury and is a channeled spell that does Chaos damage in front of you. It has a 45 second cooldown, so I suspect you'll want to use it whenever it's up. This should work nicely for cleave damage, but you'll need to make sure you're positioned so that it hits everything.
Fel Rush has two charges on a ten-second recharge that shoots you forward and does Fire damage to enemies in your path. This could be used as part of your damage rotation, though I think that will depend on how quickly you can spin back into position to hit the target again.
Throw Glaive has you... throw your glaive at the target, and it'll bounce between two additional targets, damaging all of them. This seems to be outside the Fury system, but should be nice for pulling and getting some nice cleave damage in there. It's basically Avenger's Shield without the silence.
Vengeful Retreat seems more of a utility ability, damaging and snaring targets in front of you while you jump away, though you'll be able to Fel Rush back to them if you want it just for the damage.
Metamorphosis is a whopping six-minute cooldown (though I suspect they might tweak this to lower the CD) that lets you jump toward a targeted location, dealing Chaos damage, stunning the targets within for 3 seconds, and transforming you into a demon for 30 seconds, which I believe will increase damage and enhance Demon's Bite and Chaos Strike.
Mastery: Demonic Presence increases both your Chaos damage and your movement speed, just in case you were worried the class wouldn't be mobile enough.
So at least for now, the rotation seems pretty simple.
1. Eye Beam on cooldown.
2. Chaos Strike if you're about to cap Fury
3. Throw Glaive
4. Chaos Strike
5. Demon's Bite
And possibly mixing Fel Rush in there if it won't screw you up.
The random nature of two of the core abilities may be where the complexity of the rotation is hiding. I think you'll need to watch your Fury a lot more closely than you do with a lot of other resources of that sort. And obviously, with talents and artifact traits, there will be a lot more buttons on your bars than these.