I believe that you have to do the Naz’jatar intro through unlocking essences in order to unlock the 8.3 content. (If the quest for Naz’jatar doesn’t pop up on it’s own, go to the boat to pick it up.) Once that’s done, you’ll get a quest to start the 8.3 stuff. The quests for 8.3 themselves will lead you through the various content that’s available, so you’ll get a bit of an in-game tour.
The basics for 8.3 are as follows.
(1) Major invasions. These last one week, and are a basic fill the bar quest. (Doing pretty much anything in the zone contributes to filling the bar.) Pick up any dailies in the zone while you’re doing it for a small amount of bonus currency.
(2) Minor invasions. These are pretty similar to the major ones, but they last 3.5 days, so you can do them 2x per week. Again, there will be dailies you can pick up and do while you’re filling the invasion bar.
(3) Dailies. There are daily quests in the invasion (both major and minor.) There rewards are pretty meh. Personally, I’d only do them when you’re working on an invasion. (As the daily objectives will also fill the invasion bar.) Otherwise, I’d put them at pretty low priority on how to spend your time in 8.3
(4) Mini-visions. These are up in one of the invasion zones. (I think it’s always in the major one, but I’m not sure.) These can only be entered once a day, and there’s a daily quest you can pick up right outside it that gives a good chunk of currency. These are worth doing each day.
(5) Horrific visions. These are a progressive piece of content that can be done solo or in groups up to 5 people. These are designed so that you won’t make much progress at first. (The first few times, your goal should be killing the main boss.) Each time you do them, you’ll pick up a bit of currency that will let you buy upgrades to make you more powerful inside the vision. So, the idea is that you get stronger, and can progress further.
There are also quest objectives you’ll want to complete in these to upgrade your cloak, which is a very important part of gear progression this expansion. (Wrathion will give you quests.) These quests aren’t that intuitive on what you need to do. As I mentioned the first upgrades require just killing the main boss (Thrall or Alleria.) I’d reccomend looking up a guide for the cloak and visions before you start them so you don’t lose progress.
There are two currencies you need to collect in 8.3. Coalescing visions and corrupted mementos. Coalescing visions let you buy an item to get attempts at the horrific visions. The main chunk of these will come from doing the invasions and the mini-visions. Corrupted mementos are used for upgrades to help you progress in Horrific Visions. You’ll get your main chunk of these from doing the Horrific Visions. (There are also cosmetic things you can buy with mementos, but you’ll want to fill out the upgrade tree first.)
Some of this may sound confusing, but as I said, the 8.3 quests will walk you through all of the content.
