Mox Diamond should be a Mana Crypt. Just saying.
This deck originally started as Patron of the Moon, "do silly things". Unfortunately, my playgroup at the time meant that I had to run counterspells or risk dying, as I was almost always focused (apparently I was the better player of the group, so having me dead was safer....).
Unfortunately, over time, the deck became much more unfair. The general changed twice, and more combo and control magic. It has such reached the point now where this is the deck I pull out if someone at the table is not being fun, or I feel like seeing others cry. However, it is not a traditional Azami build. It is not focused on hard combo, and deck digging for a fast win. It can play both ways. I've gone infinite on Turn 7 many times, and sometimes the game has become grindy and I've won through just having a way to never deck out.
It trades the explosive and powerful combos and a little bit of stability for flourish, showcase-y-ness, more control, and overall more resilience to aggressive strategies. It is also meant to be much more set-up based in the early stages, rather than diving into the combo as soon as possible. There is a lot of ramp, and a lot of advantage-gaining enchantments and artifacts. This deck is meant to spiral out of control in the late-game unless it is shut down early, not end the game after 20 minutes and 5 turns.
As soon as Azami comes out of the box I become a target. There is no avoiding this. Depending on the other decks at the table, the game may either degenerate into Archenemy without the schemes, or you will be able to convince the other plays that you are far from the threat, and help them take out whatever is threatening, all while building your board position and keeping all the other players's moves under check. You /will/ stab your teammates in the back if this is the route you play, just to warn you.
Early game should be spent keeping yourself alive. Keiga, the extra turn cards, and a majority of the counterspells serve this purpose; the deck's more powerful plays crave mana, and you will need at least 10 to be a threat. UUU is a combination you must have available to you at ALL times; this is what your control magic revolves around. That said, if possible, avoid making yourself a target. Play "land, go" and discard important-looking cards if need be. You don't ever need to be ahead, just never be behind. Your board position will usually be empty, this is fine. All your creatures are not for making presence. By the time you resolve a big guy you will either be aiming for a win, or simply keeping yourself alive.
Try to keep the stronger countermagic back for when shit hits the fan. Force of Will, Commandeer, Time Stop, and Pact of Negation I try not to blow when the opportunity comes. Hinder and Spell Crumple are saved for problematic generals such as Zur the Enchanter and Uril the Miststalker.
Do everything you can to set up as much as possible. Ignore incremental advantages, make allies, whatever. You need to be alive and with enough life to ensure you can get to late game. Sitting on a board position of 8 Islands, Consecrated Sphinx, and a Feldon's Cane is completely fine. The less you play early, the better - it means you get to save all your nasties for later on when people think they can stop you.
Try not to cave under pressure early on and blow your load immediately. Unless someone is really out for your blood (as I've experienced multiple times), while people focus you, another threat will rise. You can give up your crown of evil to recover position for a few turns. There are multiple lines of play, but the deck is not as hard as other combo/control decks. It is much more linear. There are multiple options for every scenario. The hardest decision is when to take on an active role and stop the game advancing for fear of personal safety, or to sit back and risk the opponent getting out of control. In short, play your counter magic wisely.
Onto the combos.
Small shenanigans / 2-card sillies:
Crucible of Worlds + Strip Mine/Wasteland/Evolving Wilds: Recursive land destruction should almost never be needed, but if someone is being specifically annoying, you can try this. I prefer Evolving Wilds to maintain consistent land drops. You can continue accelerating if you have the Terrain Generator in play.
Tolaria West + Pact of Negation/Ancestral Vision: Tolaria is extremely effective for fetching various bits and pieces.
Hinder/Spell Crumple + Tunnel Vision: As long as they don't have an Eldrazi Titan (feel free to check with Bribery), you can put target player's deck into his or her graveyard.
Consecrated Sphinx + Archmage Ascension: The Sphinx makes the Ascension online much faster. This may make you a target (as Sphinx usually does), but by the time people can stop you the Sphinx should already draw you into enough protection. Jace Beleren's +2 also helps this, albeit slower.
Rite of Replication + most creatures in the deck. Solemn, Keiga, Wurmcoil, Palinchron, Blightsteel, etc. are all stupid in multiples. Feel free to abuse this when the time is right.
Lock-down Combos:
Venser + Deadeye: For just 1U, you can stop any target thing happening. Draining Whelk also does this okay.
Academy Ruins + Mindslaver: Take control of target player forever. Needs 12 mana.
Capsize + Caged Sun/Gauntlet of Power/Extraplanar Lens: This borders on infinite mana, but in reality you do not need more than 3 Buyback'd Capsizes to start locking down the board state. Especially if you start by hitting lands, it's easy to suddenly be a turn or two ahead of everyone else.
Darksteel Forge + Mycosynth Lattice + Nev's Disk: An expensive combo to put together, but once it hits play it is almost undisruptable. Basically, you wipe the entire table, except your own. Repeatedly.
Infinites:
Mind over Matter + Azami: Draw infinite cards. There is also no risk of decking out as you can discard an Eldrazi to shuffle your graveyard back.
Planar Portal + Beacon of Tomorrows: 14 mana infinite turn combo.
Using the "Draw deck" combo above, having no deck and playing Beacon reaches the same effect without the Portal.
Palinchron + Caged Sun/Gauntlet/Extraplanar Lens : Infinite mana.
And finally;
Omniscience + Enter the Infinite : if you can't win after this there is a major problem, as this allows you to do almost everything else on this list.