I will be explaining why AD Jarvan is a great pick, and how it will help your team win.
He is very steady damage, great in team fights, and can easily make or break a game.

PROS:
Great steady damage.
Can carry teams ( I've done it Multipule times.)
Epic skins.
Not a yordle.
Not targetted much.
Cons:
Mana wh*r*.

Last hit normally, use Standard to get last hit time to time. Once your higher up just use Standard then Dragon Strike to it and minions will instantly die.

Sorry pictures are not working for me currently, add me if you want verification.
Twisted Treeline Scores:
11-5-7
9-2-10
8-1-1
5-1-1
11-0-7
Summoner's Rift Scores:
11-5-5
10-3-6
6-2-3
9-4-1

Win to lose ratio for me 9 to 1.

Greater Mark of Strength - Gives you a bit of a advantage early game, and along with your quintessences you should be getting first blood almost every game.
Greater Seal of Clarity - Jarvan uses up mana ALOT! So I go Mana regen runes so that late game I will never have to worry about mana.
Greater Glyph of Warding - Very nice runes, helps me nuke down AP and walk out with more then half health.
Greater Quintessence of Desolation - Very nice to get that armor pen in and along with Jarvans Q and last whisper you will be nuking down your targets!

Offense 23
Summoner's Wrath 1/1 - I get this for Ignite, gives you a bit of a boost and is very nice overall, the 5 extra AP and AD help out.
Brute Force 3/3 - Extra attack damage means faster killing.
Butcher 1/2 - Nice to kill off some creeps faster.
Alacrity 4/4 - Attack speed = win!
Demolitionist 1/1 - If Jarvan is left alone, he can easily push towers to victory. (Tends to be left alone, most people under estimate him.)
Deadliness 4/4 - Crit is very nice with Jarvan, along with Atma's you will easily take down your enemies!
Weapon Expertise 1/1 - Armor Pen is win.
Havoc 3/3 - More damage the better.
Lethality - If your crits hit harder, then your opponent goes down quicker.
Sunder 3/3 - Refer to Weapon Expertise
Executioner 1/1 - Damage is amazing.

Defense 6
Resistance 3/3 - Magic Resist, helps you survive!
Hardiness 3/3 - Armor, helps you survive!

Utility 1
Summoner's Insight 1/1 - Clarity does wonders for your mana.

Why did I pick the items I picked.
Doran's Blade - Health, damage, life steal. All very nice.
Brutalizer - Damage, armor pen, CD reduction. Helps you get kills, turning point for jarvan.
Berserker Greaves - Faster you hit, faster they die.
Trinity force - Everything on this item benefits you. Sheen also helps nuke down people!
Last Whisper - Armor pen and damage. No one should live.
Atma's Impaler - Most people surrender by the time you hit Sheen, but if you make it this far it gives you a bonus in Attack damage, gives crit, and armor. All very nice.
This build works for Twisted Treeline, Summoners Rift, Dominion.

Dragon Strike - Main source of damage along with armor pen. Fast CD, also good for using like a sniper.
Demacian Stanard - Throw down the flag to victory! Good for harassment, doesn't do much damage so I tend to level it up after Dragon Strike.
Golden Aegis - Good slow, a Shield. I get this fourth due to the fact that I don't get targetted and even if I do I take little damage.
Cataclysm - Level up like any other Ult. Amazing work, and people never live once the walls go down.

Your job will be to damage down the enemies, stop their escape, and stun the hell out of the enemies. Let take start it off, use your Standard first, Dragon strike in so that everyone gets stunned. Throwdown your slow, follow it up with a amazing Cataclysm ( makesure Melee are inside so they don't get blocked) People tend to go down fast!

Jarvan is a great champion, steady damage, and in general very awesome! I hope you like this build and enjoy Jarvan just as much as I do!