Maokai is one of the most if not the strongest tank in the game, it has always been a strong pick because of his powerful complete kit : reasonable damage, low cooldowns, high sustain, aoe and targetted crowd control and damage reduction previously with his ult. Maokai was recently lightly reworked which was in my opinion a nerf of the passive and ultimate (riot always had a hard time nerfing his ult so just decided to completely change it I guess). This change made Maokai a different champion to play mainly in teamfight, instead of the long teamfight survivor/peeler he was, he became a global teamfight engager with his ult and righteous glory but less of a long lasting teamfight champion.

MARKS

The only marks viable for Maokai are Magic Penetration and Attack Speed, Magic Pen are the most powerful in early game and really boosts his poking damage but attack speed scales better because they maximise the passive procs in teamfights ensuring your survival, as a tank, your survivability is more important than your damages.

QUINTS

For Quints the viable choices are AP, attack speed and armor. I almost always go AP because Maokai scales relatively well with it and that it is powerful throughout the game. I recommend trying attack speed if you are confident in your laning phase. I rarely go with armor Quints although it is good against AD strong duelist (fiora, tryndamere...)

SEALS

I always go armor seals against AD matchups and HP/lvl against AP matchup. Don't bother with the scaling armor seals. I don't recommend not using armor seals against AD.

GLYPHS

I like playing with 40% CDR so I'll always take glyphs of scaling cooldown reduction if I know I'm not reaching 30% CDR with my build (you'll only need 6 glyphs to have 10% CDR lvl 18). Against an AD take scaling magic resist glyphs if you are reaching 40% CDR with your build and against an AP flat magic resist glyphs. That said, if ever you aren't confortable with an AP matchup, forget about the cooldown reduction math and just take flat magic resist.

MASTERIES YOU SHOULD ALWAYS TAKE (in my opinion)

Courage of the Collossus is the strongest on Maokai beacase of his Q-Spell aoe low cooldown knockup, Maokai also scales very well wis maximum health. Grasp of the Undying is currently too weak compared to it. The other option viable although I don't recommend it is Thunderlord's Decree which will give you a noticable burst damage buff but will sacrifice a great portion of your tankiness.

Insight is also indispensable because it will buff TP's efficiency for teleporting bot lane or just teleporting back too lane if you are struggling.

Runic Armor, while it is not the best during the early levels, in mid/late game it will buff your passive healing, which is one of maokai's greatest asset.

Feast, on any tank you will want feast in my opinion, as a weak laner maokai beneficiates from the sustain provided by feast.

YOU CAN CHANGE THE REST AS YOU WISH

Keep in mind that tough skin won't be useful against AP laner and that Fury is a viable mastery because it gives attack speed.

STARTING ITEMS

You have basically 3 options which are :
Doran's Ring + 2 Pots : best start in my opinion although doran's shield is better stat-wise, ring gives you good damage and mana regen which is all maokai needs to sustain. You can always buy shield on a later back (recommended). Another important point is that it gives you 2 potions.

Doran's Shield + Pot / Corrupting Potion : These are other viable starts although I rarely buy them. It is all a question of personal preference. Shield is good for defensive stats but you soon miss mana and Potion will give you the sustain but you'll lack the stats.

FIRST BACKS

I recommend buying the alternative doran item you already have to stregthen your laning phase, tier 1 boots are also nice on early backs especially when you don't have tp available for your lane. KEEP IN MIND you should NOT prioritize these items but only buy them if you have gold left when building a big item (righteous glory for exemple).

COUNTER ITEMS

Against AP : Spectre's Cowl is awesome, I'll always take it in my AP matchup because it anyways later builds into Spirit Visage.
Against AD : If it is an autoattack reliant champion ninja tabi is the way to go.
If you are getting bullyed, you should consider buying these items that do great against the champions they counter.
Randuin's Omen against crit reliant champ like Yasuo and Bramble Vest against autoattack/healing champion like Irelia.

CORE ITEMS

Righteous Glory clearly the best item on the new Maokai, it allows you combined with your ultimate to engage and win game changing teamifights. The only problem is that it is a "support" item that won't give you offensive stats, compared to a sunfire cape for example that many tanks rush.

Spirit Visage is the best survivabilty items for maokai the stats and the heal buff makes you an unkillable beast once you have it.

Building these Items will give you a solid base and 20% CDR which is often all you need to win games.

BOOTS

AD teams are currently more common so you'll often find yourself going tabi.
basically buy tabi if they have 2 or more autoattack reliant champions an low crowd control threat. Go mercury threads if they have hard CC high threat (3 or more hard CC especially if they are aoe are genereally a sign to go mercury. If you hesitate with both go mercury because the CC threat is always more important than the samage.
The last option are the swiftness, you'll want to buy them when both other boots don't match the situation (rarely) or if you are really ahead to gank other lanes and help your team win the game.

CDR Items

You wan't at least 30% CDR but I highly recommend 40% and don't worry wasting gold going over 40% CDR.
In most situation Knight's vow is the best option, the utility this item currently gives just OP, remember as a tank your main role is to survive and peel your carries, make sure when buying it that no one already has it. Frozen Heart is also a common choice, I'll usually grab it when enemy ADC is getting fed or any ADC like champ (Yasuo, Master Yi...) or if my support already has knight's vow.
The other items shown above are rarely useful but basically : Go Abyssal mask if enemy team has heavy AP damage and your team too (make sure now one in your team already has it). Adaptative Helm against high threatening AP DOT damage like Rumble, this item is currently too weak in my opinion and needs special situations to be useful. Finally Zeke's Convergence is more of a fun pick, if you wan't to scare your enemy with an all in Maokai build you can buy it, if your adc is carrying its also worth buying with knight's vow.

Final Items

I almost always get gargoyle stoneplate, I think it is a great new item that finds its use in every situation. If I have space left I'll prioritiza Omen or Thornmail depending on the situation (VS Crit for Omen and VS healing for Thornmail). Zz'rot and Dead man's Plate are more fun picks but can prove to be useful, Zz'rot can be used as a split pusher to seperate enemy team if they have a stronger teamfight than you and Deadman's plate is nice if the enemy team has low armor and that it is a "roaming" game.

Maxing Q spell is the most effective way to survive laning, although some Maokai players count mainly on the E sapling toss as a source of damage (since the Maokai rework), I find that approach easily counterable and your success will be random, I thinl maokai's E is his worst spell and that's why I only put points in it at level 8 it has a high mana cost for damage that are only viable when casted in brush, I'd say I even preferred that spell before the rework because it did more damage out of brushes and did damage at landing. That said, the E is very effective to act as a ward so if you are getting camped, put points in it before level 8.
There is not much more to say about the choice of your skill sequence, I find that this one works the best, I always take my Z twisted advance on level 2 because it can faciliate early jungler ganks. Don't bother starting with your Z if you invade because of the targetted CC and don't bother starting with your E to help your jungler.

Passive Sap Magic
The ability that makes Maokai so hard to kill, with the rework it was nerfed in early game but still strong in late. Your Sapped autoattack will heal you for 13% of your max HP every 20 seconds at level 18, the cooldown is reduced by 4 seconds everytime you'll get hit by an ability or cast one. In late game teamfights, the passive will proc several times in a short time making attack speed so effective on Maokai. If you keep track of this ability, you can use it to surprise your enemies who think they are about to kill you. Remember your spells also reduce the cooldown of it so spam them in situation of crisis.

Q Spell Bramble Smash
An AOE knockup + slow that slows also the ones touched by the short ranged projectile. It is what makes Maokai so solid and reliable in my opinion. This is a low mana cost, high damage (for a tank) and low cooldown ability. It should be spammed without thinking. This ability is the one that will proc your keystone mastery shield. It scales ok with AP. This is a cast ability so it means your character will have to stop to cast it and will cancel your autoattack animation, it can be flashed to surprise your enemies, simply start the animation and flash instantly after.

Z Spell Twisted Advance
Maokai's most interesting spell it is a low damage medium cooldown and medium mana cost gap closer that will snare your target upon hit and gives makes you untargetable will dashing. The untargetable part of it is clearly the most interesting, once you'll get used to the timing of it you'll be able to dodge crucial abilities like Yasuo third Q spell keeping him from ultin you. The snare is very useful when your jungler ganks you or to catch enemies, I never hesitate flashing + Zspell on isolated carries if my team can follow up and kill him. In teamfights / ganks I recommend keeping it available and use it wisely, if your jungler ganks you don't engage with the Z spell but try to keep it for the end and during teamfights instead of diving for their carries that you won't kill alone keep it to peel for your ADC.

E Sapling Toss
Maokai's worst ability in my opinion, the only use I find it is the vision it gives. You can build your items around this spell and max it first but it isn't a garanteed success. Keep in mind it has a relatively high mana cost.

R Nature's Grasp
Maokai's new ultimate, it made Maokai's playstyle different, it has relatively high damage and a snare, the only problem is the time it travels at that is very slow so before engaging alone with it I recommend Having bought Righteous Glory to make sure the enemies get snared. It is also good for disengage and the cooldown is low for an ultimate.

Basically as Maokai with this build you will want to survive laning phase, roam in mid game and peel your carries in late. I don't like to say Maokai is weak in lane because he is actually quite strong but he just has a low kill potential, you'll get most of your kills from ganks and you shouldn't greed and overextend because you have a very low pressure and are vulerable to ganks. I know it is hard not to push with maokai since you'll be poking the enemy with Q spell that will eventually push lane. Don't hesitate using your TP back to lane in early game.
In mid game the fun starts once you have your ult + Righteoous Glory you shall start roaming and applying map pressure the best you can do is countergank other lanes to ensure double kills and push objectives.
Once in late, you'll want to always be with your ADC, engage fights but not dive leaving your team alone, a mistake a lot of tanks make, maokai has one of the best kit for peeling, use it.

Pros

+Insane Survivability (lane and teamfight)
+AOE and targeted hard CC
+Strong engage
+Great peel
+Low cooldowns
+Vision providing spell

Cons

-Low kill pressure
-Only 1 actual damaging spell
-Weak without rest of the team
-Hard time laning against ranged