Now I'm of two minds about this.
On one hand, Enhancement has, for over a decade, been a weird spec. It has used most of the same toolkit that Elemental had, but used some special mechanics to allow it to function as a melee class.
When I first started playing World of Warcraft, Shaman was the first class that I really played with any real intention of leveling up. (I had created a Paladin on the wrong server and then found out my college roommate was playing Horde, meaning I'd have to switch to a different class. I mean, who ever heard of a Horde Paladin, much less a Tauren one?) The class that I always wanted to play was an archetype that I always considered a standard RPG option but somehow have not been able to find anything that quite fits the description in basically any game I've played, namely the Battlemage.
Heavy armor, a big heavy weapon (preferably a war hammer, specifically the unrealistic sledge-like maul variety like Hammer of the Naaru or The Black Hand,) and blasts of arcane magic sundering my foes.
Enhancement Shamans were not exactly that, but they came pretty damn close (in vanilla Enhancement used two-handed weapons. And Strength as their primary stat. It was a weird time.) It actually wouldn't be until Wrath of the Lich King that the spec really delivered on its promise, though, using Maelstrom Weapon to allow us to cast Lightning Bolt and Chain Lightning in the middle of combat.
In fact, using a lot of Elemental's kit in melee was kind of exactly what those of us looking for a Battlemage class or spec were looking for.
But there were some issues. For one thing, Enhancement has had a weird relationship with Mana, leading eventually to Warlords, where it's just a blue bar that means nothing, more or less. Enhancement has always been about simply juggling cooldowns, and it seems like they've made up for a lack of alternate resources by simply giving you about three billion abilities to juggle.
In Legion, Enhancement is getting a massive overhaul. You'll still have Windfury procs, you'll still have Lava Lash and Storm Strike, and you'll still have your Feral Spirit cooldown, but almost everything else has changed.
Both Enhancement and Elemental, who had basically ignored their mana bars for a long time, now have a new resource called Maelstrom, which they build somewhat slowly (slower than Rage, but not terribly so) and use to hit their hardest attacks. Enhancement generates a lot of this through abilities, but also some through auto-attacks thanks to the Maelstrom Weapon passive (which has nothing to do with the old one.)
The old weapon enhancements (minus Windfury, which is just a passive buff now) have transformed into active abilities, which I'll go over individually. These each are technically ranged attacks, but have a mere ten yard range, so you can basically treat them as melee attacks that are forgiving if the enemy is moving around a lot. Two of these will be your main Maelstrom generators.
This is your absolute bread-and-butter attack. You hit the target for some physical damage and generate some Maelstrom. This has no cooldown, but you can switch it out for Boulderfist if you want to retain some downtime gaps in the rotation to use on utility or simply give your fingers a second to rest every now and then. There's also a talent that makes this more like the other weapon-enhancement-named abilities and makes it buff you.
This one is on a cooldown but also gives you a buff that makes your attacks do additional fire damage - it's a maintenance buff but has a longer duration than its cooldown, so you've got some flexibility for it, and it also generate Maelstrom.
This one is A: mostly just utility, causing your attacks to slow the target and B: costs, rather than generating Maelstrom. This won't be part of a normal PvE rotation except with one of the legendary items and possibly one of the talents.
Your only true melee strikes (though again, you can count the Weapon Enhancement abilities as practically melee attacks) are Lava Lash and Storm Strike. These cost Maelstrom and hit harder.
No cooldown, this simply costs Maelstrom to do fire damage to the target, I think still using the off-hand weapon (which with the Doomhammer is the lava-themed Fury of the Stonemother.) Just as Rockbiter is the "filler" for Flametongue, Lava Lash fills in when Storm Strike is on cooldown. There is a talent that makes this occasionally free, which will probably mean you'll be seeing it a lot more in your rotation (see below.)
The crown jewel of the rotation, Storm Strike hits hard but costs a lot of Maelstrom and has a cooldown. However, there is a proc that resets its cooldown, cuts the cost in half, and prevents I believe the next two Storm Strikes from triggering a cooldown. This means you're often going to want to pool Maelstrom so that you can use Storm Strike as much as possible - probably just saving Lava Lash to burn off Maelstrom if you're in danger of hitting the cap.
This is instant-cast and I believe has no cooldown, but is really just for pulling. There is, however, a talent you can pick up that increases the damage by a huge amount but also makes it cost Maelstrom and have a long-ish cooldown. I think with this talent Lightning Bolt will become a pretty high-priority spell, if not the top priority.
This is your on real AoE ability, but it does multiple things for you. First, it hits every target in a pretty wide cone in front of you with nature damage (and can be talented to leave a little electrified patch - a kind of Shaman Consecration.) It also gives you a buff that causes your Storm Strikes and Lava Lashes to hit everyone near your target. This costs a somewhat low amount of Maelstrom, so I think it's probably meant to be used in any situation where there's more than one enemy to hit.
One really odd thing is that there are WAY fewer Totems to use now. There is one entire talent row with all totem abilities, and one other talent that transforms Hex into Voodoo Totem (which Hexes anyone near where you place it,) but there is not, actually, a single baseline totem for Enhancement.
So to break down the rotation, before we mention talents and such:
Stormstrike whenever you can.
Lava Lash if you're going to cap Maelstrom and Storm Strike isn't available.
Keep the Flametongue buff up.
And for multi-target situations, probably top priority is to maintain Crash Lightning's buff.