I've been playing JarvanIV for a while now, and I must say... He is a 'beast'. Not only does he have a decently fast jungling, hitting level 4 at close to 4:30-5:00 in, but also has the capability to do amazing ganks that can almost guarantee you a kill.

He has been overlooked on the radar for so long... I believe it's his time to shine in the jungling spotlight.

A standard Jungle Set is fine.

My rune set is

9 - Greater Marks of Desolation
9 - Greater Seals of Resilience
9 - Greater Glyphs of Shielding
3 - Greater Quintessences of Desolation

This gives me an easy time cruising through the jungle, and the armor and magic resist give you just enough protection for that early gank if you're 'VERY' eager for that first blood.

Alternatively, you can substitute Resilience seals for Evasion and your Shielding glyphs to Resilience as well if you really want to. It won't affect your jungling/laning possibilities, but it is all based on what you want and how you want to play.

- As a side note, the less armor you have at the beginning, the harder it will be for you to go through your jungle.

To be honest, it doesn't really matter what your mastery setup is like.

I run 21-0-9.

I hit smite and all the other damage upgrades in the offensive tree.

I hit ghost, exp and one point in buff.

This set up allows for an extended ghost, chase-getaway, and a more offensive style of play for those who choose not to be so aggressive and like to keep up the poke once in a while.

Cloth and 5 Pots
Pretty self explanatory I think... Well I mean like... yeah... Jungle stuff... Simple... No?

At this point, on your first back depending if you want to keep jungling or ganking, you can choose to go for boots to gank, or a long sword for quicker jungling.

I would suggest to you finishing up those Madred's Razors and then finishing your boots and back again to finish your Wriggles, but you can also finish wriggles first before finishing your tier two boots.
-Note please please please, if you must rush wriggles, please get at least tier one boots before completing it, or you will be constantly ganked in your own jungle unless you're in a premade of 5 and are aware of every enemy champion's position at all times.

At this point with Wriggles+(Your Choice of Boots) you're pretty well off and can deal some decent damage.
From here, you can either go do Trinity Force>Atma's>Warmogs>Banshee's/Guardian

OR

You can go Frozen Mallet>Atma's>Warmogs>Banshee's/Guardian>Phantom Dancer in place of Wriggles.
-Note Phantom Dancers replacing Wriggles is optional, but the extra move speed and extra critical hits will help you finish off those pesky douchebags that just won't die. But remember, the movement speed and critical hits come as a tradeoff for armor, life steal and a personal ward. The choice is yours as both are perfectly fine.

Please be advised if you're not doing so well;
Do not, I repeat, do not try to go for Trinity force. If it so happens that you aren't doing well at all, start off with a Catalyst instead and get a Chain Vest, with these two items you should be okay for being half tanky and a decent amount of damage due to your passive. Finish off the banshees, and make that Atma's. At this point it's your choice to finish up Warmogs first or Trinity. I would suggest Warmogs first because of your poor early game, being a bit tankier mid/late game will help a lot. Finish it off with a Trinity and you'll be fine for the rest of your game.

Hah! Now this is a quite a pain to decide and think through.

E>Q>Q>W>Q>R>Q>E>Q>E>R>E>E>W>W>R>W>W
This Skill Sequence allows you to go for a more offensive... fine I lied... this sequence is the most offensive sequence you can do with Jarvan IV. You will be taking out armor like nothing when you land that E>Q combo. The low cool down makes it almost spammable late game, and you will 'HIT' hard at every point in the game if you do this sequence.

E>Q>E>W>E>R>E>W>E>W>R>W>W>Q>Q>R>Q>Q
This Skill Sequence allows you to play a bit less carefully. You may make a mistake or two, and it may not result in your death, but warn you that you may be very close to death so beware of those sneaky Twitches/Evelynns/Shacoes/Karthii/Nocturnes or any other champ that is a sneaky douche-bag.

-Note Jarvan IV's passive is OP, so ABUSE it. When you find the chance, smack the other champion upside for 8% of their current health. Show him who is BOSS.

Smite
On a jungler... You can not... and I repeat you can not jungle without this... Need any more explanation?

Ghost
It's the only thing that I can choose within the first 9 options of the Utility Tree, so bite the bullet and take it!
On a more serious note, this Spell gives you great ganking ability unlike other junglers that need to be right up in the other face of the champion to initiate. With ghost, Jarvan IV can run at a different angle and throw in an E/Q combo to cut off a running champion. And after that once they're knocked up, put down that E... and... well... you know... they're slowed... and you're still in ghost... it is like... outrunning some fat chick... it is stupid and they're dead unless they ghost and flash... which is also good because they wasted two of their summoner abilities for one of yours.

They only reason why I would take flash is for trapping enemy champions.
Let us say that one of our friends are on the run... they're almost dead... they beg and cry for you to help... if they don't... then tell them to shut the **** up and die... and back to the point... if you ult them and you have no mana left you can flash out of your own ult causing them to be stuck there for a good 2-3 seconds more than enough for you to escape and your friend to escape.

Other than the aforementioned Spells I wouldn't suggest any others.

You wouldn't need Exhaust at any point... unlesss you're not jungling... which is then okay... but... your damage output is beyond belief... and it's honestly useless to you.

You wouldn't want ignite either... I mean... why rely on such a ****ty last hitter, when you burst people down into nothing in seconds... If they do get away... well then... tough luck buddy, cause you messed up somewhere...

I don't need to explain Clarity/Clairvoyance/Cleanse/Teleport/Heal/Revive/Rally do I?
I mean like... Clarity is for you know... Supporters... and you're... tanky DPS... so no.
Clairvoyance is also for you know... Supoorters... so no...
Cleanse? Well I'll admit it's a good spell, but if you get caught in a lot of crowd control... I did tell you to buy Mercury Treads and suggested Banshees didn't I?
Teleport/Heal/Revive/Rally At no point in the game will you EVER be backdooring so please don't use these stupid spells and think because I'm godlike I'm going to revive/heal/teleport/rally and backdoor some turrets... You're not a ****ing Yi, but if you do find a Yi, you will be ****ing him up all day long. I mean lets just compare the size of our weapons and end it at that. Hah! My ***** is bigger than yours!

Jungling Route
Start with a leash at blue, if someone can strong leash it then good.
Standard route, just finish everything in one go, if you can't then skip red, but finish the twin golems at the other end and back. Then come back and finish off red and you're good to gank.

Ganking!
Please do not try until you are level four, or atleast have a point in W. Otherwise you will charge in like a fool, and people are going to tell you that you fail at ganking scrub.
Please make sure that when you are ganking, the other is aware.
Now onto the tips of how-to-gank Jarvan IV
-Aim your E infront of them, it doesn't have to hit them, but it needs to be placed in a way that when you Q you can charge in and knock them up... that is important... let me repeat... your E DOES NOT HAVE TO HIT, it just needs to be in a position so that your Q will let you knock up the enemy champion. After that, just put down W and they're slowed... then knock away with your giant *****. It should be a guaranteed kill if your ally in the lane you ganked is aware and helping out.
-as a rule, if they are 2/3'rd of their HP or more, it's best not to gank and go in for a kill, but gank only to show lane presence.

Choosing when to ULT.
Most of us are probably familiar with people blaming Jarvan for a bad ult because he locked his allies in and they died.
This is honestly one of the more peculiar ults... there is no correct placement... but the most ideal time to ult or to use your ult is when you can for sure isolate a dps/support/healer/ from a teamfight completely rendering them useless as the rest of your team takes out the other four. On the other hand, if your team can not do it without you, you will not be able to ult like that, and you will probably never be able to ult in a teamfight if your team cannot fight without you. If that is the situation, save your ult until after the teamfight starts to lose its steam and when they start to back, ghost in and ult them and it should be a guaranteed kill, but please do so in your own discretion.. don't ult an oponnent while you have no life and trap in your own allies with no health and get pentakilled for being a moron.

And that's about it.. well... what are you waiting for? You're the Prince of the Jungle... get back into it... ****ing tree-huggers.

Good luck with your games.