Council page on the wiki
Councilors page on the wiki
Committees page on the wiki
The Council is a money grab building in some way similar to the Museum, but with different mechanics. Like the Museum, you have some amount of control over which bonuses you get. And like the Museum, you have to work for the Councilors (and associated Committees) that give the bonuses you care about.
Simply stated, you get bonuses in the Council by assigning Councilors. And certain combinations of Councilors create Committees, which give additional bonuses. So you have to look at not only the bonuses on the individual Councilors, but also the bonuses on the Committees.
There are several way to obtain Councilors. The most prominent are:
So, you have a bunch of Councilors. When you look at them, you'll see that most of the bonuses are not active. Councilors are divided into:
However, unlike the Museum where you can upgrade your artifacts, you can't upgrade/unlock your Councilors. Instead, you "Fuse" them. Fusion is the process of combining three Councilors to (maybe) get one better Councilor. Every time you fuse Councilors there is a chance of getting one of a higher rank, but usually you'll get one of the same rank you started with. AND, the Councilor you get is random. So it isn't like you can fuse three Alexander the Greats and get one better Alexander. You'll just get some random Councilor, which might happen to be an Alexander, but probably won't be.
People were really fussy about the Council when it first came out, so they added a counter where after you fuse Councilors at a given level 25 times, you're guaranteed to get one of the next level up. You can see this little counter on the left side of the Fusion screen - there's a counter for each level. This means that you should fuse regularly. Not only might you get lucky and get a better Councilor, but you're guaranteed to be making progress toward a better one. It might not be the one you want, but you at least have a chance.
People were still fussy even after that, so they also added rewards that you get after discovering different levels of each Councilor. When a reward is available, you'll see a special little icon on your Council. Click it to open the screen that lets you claim. At first, these rewards are kinda lame - a few crowns or the same kinds of Councilor lootboxes you get lots of other places. But eventually a magical thing happens. You get a Mythical lootbox which gives you a bunch of really good Councilors all at once. Unless you're really unlucky, you'll get a least one Legendary, and maybe several. And opening these will probably give you enough new discoveries to get a whole bunch of crowns. Use them to reroll any Legendaries you get to make them be whatever you really want. "What's reroll?" I hear you ask. Well...
When you get a Epic or Legendary Councilor, you also have the option to "reroll" it to get a different Councilor of that same level. So maybe you really wanted Alexander, but you got something else. You can spend crowns (starts at 500 and goes up with each reroll of that particular card) to try again. You can decide for yourself whether it is worth it to reroll Epics. I haven't done that, myself. But I did spent a bunch of crowns rerolling the Legendaries that I got out of my Mythical chests. Which didn't cost me any real money, because I had just gotten a ton of crowns as a reward.
The problem with the Council is that (unless you spend real money) it takes a long time to build up. Assuming you don't get lucky and just happen to get a Legendary Councilor out of a lootbox or something, and ignoring the occasional lucky next-level-up card when fusing, then here's the math: it takes 75 Commons for each Uncommon (fusing 3 commons 25 times), 75 Uncommons for each Rare, and so on. So 75x75x75x75=31,640,625 Common Councilors to get one Legendary Councilor. Wow. At five Common Councilers per day, that's over 17,000 years. Now you see why I called it a money grab. People willing to spend lots of real life money on Legendary Councilor lootboxes (which only have very small chance of giving a Legendary) are going to have a huge advantage over people like me, who might drop a few bucks here or there on the game, but who aren't going to spend hundreds or thousands of dollars (or even more) at a time. That's just life, I guess.
Now, in practice it isn't nearly that bad, because you do get an Epic from a lootbox or when fusing Rares now and then, and each Epic is the equivalent of just over 200 years of recruiting and fusing. But still - don't expect to build your Council and quickly stock it with Legendaries. But also, don't despair. Recruit and fuse regularly, work your way up through the rewards, and you'll eventually get the Mythical lootboxes. Do some rerolling with the reward crowns and you'll have a decent Council, if not an ideal one.
The Council has an additional sneaky advantage, at least for now. Unlike the Library, University, and Museum, there's no way to "Spy" an opponent's Council in war. That's probably just because the Council was introduced after the Spy feature, and there was therefore no University research for unlocking the ability to spy it. I wouldn't be surprised if a future update added the ability to do this (and if so, you'll probably have to spend a lot of time and resources unlocking it). But for now, you opponents have no idea what's in your Council.
This also gives you a good excuse if you lose a war attack you should have won. You can always say "they must have had an awesome Council". Okay, I"m just kidding about that part.
We haven't talked about Committees yet. Basically, Committees are just extra bonuses you get by appointing certain combinations of Councilors. Because you can't really control which Councilors you get, obtaining the right set of Councilors for a particular Committee is a matter of luck, plus however many crowns you want to spend on rerolls (which is still luck, but at least gives you a better chance to get the ones you want). Here's how I approached Committees. First, I equipped the Councilors that gave me the bonuses I cared most about, without worrying at all about Committees. Then I opened the Committee screen and checked which I was pretty close to completing that had bonuses I cared about. Then I evaluated whether it'd be a net gain or loss to swap out a couple of Councilors that had less great individual bonuses, but which gave me better Committe bonuses. Personally, I only ended up swapping one.