Welcome to my Guide, actually this is the first I create.
This is the way i play Jarvan like he is/was right after he was published(Until now there are no Changes)
Well, why should i write a book here.. the most of you won't read this at all =)

Pros:
Awesome damage output
Damage ampifier - even without Items
Free 8 Second Ward with E (use it to check if Enemies hide in the Bush
New Champ -> Surprise the Enemies with your Abilities

Cons:
Mana starved, Blue golem addicted
F*cked when CC appears
New Champ -> get often focused

Well, as I´m new here, i don't know how to bind the Runes in here. But you can check them on Top.
Greater Mark of Desolation - 9x for good Armor Penetration Early, Mid and Late Game.
Greater Seal of Alacrity - 9x Nice Attack Speed combined with your passive/active E and Items = Effective Madreds
Greater Glyph of Focus - 9x to reduce your relative long Cooldowns
Greater Quintessence of Desolation - 3x even more Armor Penetration = more Damage Output

I like to Start with Dorans cause of the Armor, Life Regen and Hp it gives, you´ll hold the lane longer until you can affort your Boots of Speed and your Vampiric Sceptre, if you get Kills early for Madred's Razor,too.
After i got Madred's Razors i´ll get the Blue Buff as soon as possible, because in early Game you´ll have some troubles with your Mana, and even the CD this provides is just a advantage.
Then i go for Boots of Swiftness. Why? Cause Jarvan is a damn slow Champ. Easier to get to the Team or to run from Enemies.
Get Phage after it to get some Attack Damage and Life + the passive which helps to get fleeing Enemies. Then you should buy Recursive to get more Attack Speed, until now you should have enough Dmg, you don't need more.
Finish Frozen Mallet first for the Passive and more Life. You´re able to fight the Enemies easier and they cant flee anymore (excepting Summoner Spells)
After this you finish your Madred's Bloodrazors - combined with the Attack Speed you´ll have you take the Life rapidly down.
Now to get more Damage and kill even faster, buy Black Cleaver to get more Attack Speed and Armor Penetration, then finish Bloodthirster (remember the Vampiric Sceptre at begin?)
This helps you to keep your Life up ( you´ll deal gooood Damage)
At last i recommend Banshee's Veil to counter the Spells (especially CC) or Guardian Angel if you think you die too fast.

Remember : You´re not an Tank, you´re the one who deals the Damage and rape the Enemies down.

Well this is my short Build, but i hope you like it.
PLEASE let me know about your Opinion about my Build and Ideas how to make it better.
Regards RebornNoob (feel free to add me In-Game to discuss something with me.