Alright, so I have a pretty big info dump incoming, a lot of info might be a big help to let you know what to expect, so bare with me. I think it's also important to mention in terms of the endgame, if you've not experienced it yet, is that as the new patches come out you'll want to make sure you keep up on both the MSQ progression and take note of then complete any future sidequests that will inevitably unlock new dungeons. The sidequest dungeons may technically be optional content, but you will want to make sure you do them because they will be required to do the expert roulettes. Expert roulette consists exclusively of the most recent few level-capped dungeons, and are one of the most essential ways of getting your endgame tomestones. By now I'm sure you've been making use of the Tomestones of Poetics obtained from doing content from previous expansion endgames. If so, you'll be aware that they are used to purchase the base forms of some of the best gear from those expansions, as well as items to augment them to higher ilevels. The current endgame works similarly, but there are notable differences.
Once you've caught up with the story and gotten to level 80, you'll have two types of tomestones for the current endgame. At this time, the first type are Tomestones of Goetia, which are used to obtain i440 gear that's slightly better from the early level 80 dungeon gear drops. You can hold up to 2000 of these, and there's no limit to how many you can obtain in a week. As long as you keep spending them when you max out, you can farm these tomestones as much as you want. The gear obtained by this particular kind of tomestone cannot be upgraded, however, so you'll probably find many of these being replaced quickly as you progress. The second and more relevant kind of tomestone at this time is Phantasmagoria, which is used to purchase i460 gear, and while you can still carry up to 2000 at a time you can only collect 450 of them per week. This gear can be upgraded by trading a piece with its respective kind of upgrade item, however unlike with the Poetics gear from older expansions you can only obtain these upgrade items in limited and specific ways. The easiest methods being clearing the new 24-man raid to obtain a tradeable coin once a week that you can trade for one upgrade item per coin, or by unlocking and doing the current expansion's hunts to farm the special currency obtained from them to purchase an upgrade item. The other way to obtain an upgrade item is by doing weekly clears of the second and third savage fights from the current tier: Doing so will give you a chance to either win one by rolling for it, or you can collect four of the books you obtain once a week for clearing either fight to trade for the respective items. Now, if you're doing casual content it's not super-necessary to upgrade the gear to i470, but as long as you do your weekly 24-man clears it shouldn't be hard to get most or all the tome gear upgraded without the need to do savage content, and will help you stay ahead of the ilvl curve to ensure you aren't gated out of future story content which will require higher-ilvl gear to progress in later patches.
Another important source of gear is doing the normal versions of the current 8-man raids. These may be a bit harder than typical story trials, but still very doable for casual players. When you clear each of the four fights, you'll be able to roll for items to trade for i450 gear, which is decent enough, but you can only win one piece per fight, per week, so choose wisely. For example, the right-side jewelry pieces typically only require one of their respective trade items, while things like pants and chest pieces require four of their respective trade items. Also, when you clear the last fight for the first time each week, you'll get one special trade item automatically. For now, I think you still need seven of these plus 1000 Tomestones of Phantasmagoria to buy ten of the other trade items to obtain the i460 weapon, which can be upgraded to 470 eventually. When it gets closer to 5.2, eventually a lot of the fight lockouts will be removed, so you can farm the trade items more easily, and you'll only need four of the weapon trade item you get from the last normal raid fight. It's also important to note that the new 24-man fight also has i460 gear drops, but for now you can only win one piece of gear per week. This restriction will also be lifted over time, however.
Basically this will be the pattern throughout the expansion, though things will start cycling out. For example, there should be new 8-man raids in patches 5.2 and 5.4. When 5.2 drops, the Tomestones of Goetia will stop being obtainable, and Phantasmagoria will essentially take their place. The i440 gear will likely be only obtainable then through hunt seals, and the i460 gear will take their place at the endgame hub, while a new type of tomestone will take the slot Phantasmagoria was in to trade for higher ilvl gear. The i460 gear will still be upgradable to 470 with the same items, unlike the i440 gear which will still never be upgradable, and the new tomestone gear will also be upgradable through similar means as the 460 with their own set of upgrade items for their current tier. The 24-man raids should also be continuing when 5.3 and 5.5 come out, and will work in a similar way to the current 24-man raid in terms of item and gear drops. As for the Goetia, once those are discontinued, you will have a chance to go to Mor Dhona to exchange them for a certain amount of Phantasmagoria, which will become the new "unlimited" endgame tomestones. Evetually, Phantasmagoria will be cycled out the same way, and so on as new content is released.
The extreme fights, while also harder than the story content, are still generally accessible to more casual players. There are currently three in the current expansion, one for each of the current story trials: One drops i450 weapons, one drops i450 accessories, and the newest one drops i465 weapons! Also, each time you clear one of the fights, they drop totems that can be collected and then exchanged for any of their respective gear drops. Unlike a lot of endgame content, however, there's absolutely no lockouts involved with the EX fights, so once you're able to beat a fight you can farm it as much as you want, as long as you have a willing party to help you out. EX fights also have a chance of dropping goodies like mounts and items used to craft the music scrolls for their fights as well as for housing items/chocobo bardings/minions. The craftable items on their own tend to be very sought-after on the market boards, which can be another incentive to try to farm for them. The mounts are the biggest deal, since you can't get/sell those on the mb, and though they tend to drop rarely you will eventually be able to trade a whopping 99 totems for them as the fights get older. In terms of the expert roulette, also keep in mind that likely starting in 5.2 that the older lvl80 dungeons will start cycling out of that roulette to be replaced by the newer dungeons, at which point there will likely be a new lvl80 roulette for the dungeons that get cycled out. These will also become good sources of endgame tomestones. Also, another bit of gear to be aware of is the crafted gear that comes out around the time each raid tier drops. This gear tends to be just high enough in ilvl to handle to hardest fights of the current raid tier, and also has the added bonus of having five slots to meld materia in! Unfortunately, materia melder NPCs can still only meld for two of these slots, so you'll either need to have the ability to meld materia yourself at that level or have a friend who can meld it for you. Materia helps to boost your stats, but if you're doing casual content, this may not be too important to you. However, if you want a quick way to have respectable gear and have either the ability to make it yourself or the gil to buy a set from the mb then it's definitely a good option.
In short, as long as you are diligent in doing the MSQ, unlocking dungeons and 8-man normal/24-man raids, do your weekly runs, and cap your weekly 450 endgame tomestones, you shouldn't be hurting for gear. I all seems like a lot to take in at first, but once you start getting into it you'll find it's easy enough to keep up with. This is still a great time to catch up, since we're still early in the expansion, so once you do hit endgame it won't take long to catch up to the latest content. And with that, that's all I can think of for the moment of what to expect with the endgame. Of course, if you're looking to get into savage/ultimate content there's just a little more to it, but not a whole lot.