Blue -> Wolves -> Wraiths -> Red -> Small Golems -> Gank.

You NEED blue to jungle before you have RoA, after RoA you can give it to the rest of your team.

Red is needed for pre-6 ganks, post-6 feel free to give it to whoever needs it, although it will make your post-6 ganks basically OP if you do choose to get it.

Pros:
-Super Fast Clear
-IMMENSE post-6 ganks
-Incredible Invade
-Snowballs to become stupidly godlike late game.
-An incredible late-game off-tank.

Cons:
-Pre-6 ganks are kinda "meh".
-HIGHLY blue-dependent. Make sure you get it.
-A weak early game and a not too brilliant mid either. Its his late game and ganking strength NEED to be abused.

This set will give the fastest, safest jungle time. The MR/lv are fantastic throughout the entirety of the game as well, especially as the core build does lack in MR.

Alternates:

Magic Pen Marks/Quints -> More damage late game, but makes jungling dangerous.
AP Glyphs -> Even faster jungle and stronger pre-6 ganks.
AP/lv Glyphs -> A massive boost to your lv6+ ganks, I personally prefer the additional MR for late game but these are my second choice.
Movement Quints -> Always good, stronger ganks but the AS loss will hurt jungle times.
Flat AP Quints -> Slightly worse in the jungle, slightly better in ganks and towards late game, your choice.

Pre-6:

ONLY use the flash before 6 when ganking if it is sure to net you a kill you would not otherwise get.
Get as close as you can without being seen then activate your exo-skelleton and run in and try to get a Q hit off, then keep pace with them AAing if possible and using your Q to slow as soon as it comes off cooldown. If you have red then just right click and hammer the Q button. Use E when you can if you have mana for more damage. Use flash ONLY if they escape somehow (flash/CC) and you need to deal that one last hit or slow them for the kill.


Post - 6:
The same as pre-6 but for a more lethal gank if they flash away when they see you flash onto them, hit Q once then R and dragg them to exactly where your team needs them, eg on top of the malz/morganas AoE or near a wall for poppy/vayne/alistar. The best bet is usually towards the turret. Then if you have Blue buff your Q should come off cooldown just as R finishes giving you a slow. Then just continue AAing and Qing until their dead. Virtually no champs can survive ganks of this strength if you have a decent team-mate. Flash is ofc not neccassary and I only use it if either it would save an ally, allow me to drag an enemy under a turret or if my target uses flash to escape themselves.

The Cloth Armour unfortunately is going to sit alone until you build madreds, if you even build it at all. It isn't ideal but it gives the best jungle.

Situational Items:
Oh sh*t we don't have a tank cos that **** lied/changed his champ last second! No worries scarner is pretty damn viable tank if he has to be. He isn't really a main tank but if you get stuck like this then your going to want to get items from the 2nd build in whichever order you need, although RoA is still Core.

OMG AoE team! Abyssal Sceptre & witts end are great if your against a full AP AoE team. If its against a more mixed AD/AP team (mf/gp for example) then zhonyas is a good bet. Make SURE one member of your team at least has an Aegis of legion. If they don't then grab it yourself.

Dat AP carry! Fed AP means a witts end straight after your RoA and sometimes get banshees too if I'm really struggling but usually after another core item. EG:
Mercs -> RoA -> Witts End -> Guinsoo's -> Banshee's -> Nashor's/Rylais

Dat AD carry! This is a bit harder as AR items tend not to stack as well with scarner but their are a few. Madreds Bloodrazor a bit earlier will help, but its too expensive to be relied on. Grabbing a Frozen Heart instead of Nashor's is probably your best bet, you still get the needed CDR and 99 AR & -20% AS are usually going to be enough. EG:
Merc's -> RoA -> Glacial Shroud -> Guinsoo's -> Frozen Heart -> Madred's Bloodrazors -> Rylais