This guide is not meant to be a "MY BUILD DA BESS" kind of guide. There are many other successful builds out there that Jarvan can perform well with. This build just happens to be the one I like.

This build isn't really meant to kill. It's meant to:
-Initiate
-Create dissonance in enemy strategy
-Tank, knock up, and slow for the team while dealing substantial damage

I generally do end up with a positive KD, and I do die, but let's say my best record so far has been 11/9/34. (I was there for 45 of my team's kills with the total kill count being in the 60's.)

So don't expect godly kills and minimal deaths. You might as well expect negative KDs at some point. This build stresses the team player role. Don't chase for unnecessary risks. Prioritize your teammates over your opponents. Time to begin.

Pros:
-Great team player.
-Not too squishy when it comes to early game.
-Nice harassment skills.
-Knock-up, slow, and trapping utilities.
-Very tanky late game with decent damage.
-Tank turrets like there's no tomorrow.
-Can break teamfights if played properly.

Cons:
-Often the first target when it comes to pre-minion fights. You are a big threat, after all.
-Slightly difficult to kill on your own late game.
-Slightly mana hungry early game.
-Dependent on laning partner to thrive throughout the game.

Some of you may find my mastery build quite odd. 1/14/15 are very odd compared to the 21's and 9's you often see. I do have my reasons, however.

Offense: 1
One in Cripple for the Exhaust buff is all you need. All of the other Offense masteries are quite negligible to your performance.

Defense: 14
The Armor, Magic Resistance, Dodge, and 2-in-Health Masteries give you more bulk to start off with early game. I would spend the two in Veteran's Scars and one in Harden Skin somewhere else, but nothing else appealed to me. AP, attack speed, and 4% damage reduction isn't much, so I didn't bother with those.

Utility: 15
Three in Good Hands because Perseverance is useless. One in Haste for the Ghost Walk buff. Four in Awareness because 5% extra mana is useless. One in Greed because the extra money doesn't hurt. Three in Meditation to support your early game mana needs. Three in Quickness for that extra chase or escape. 6% cooldown and decreased cooldown on summoner spells is useless for this build, so I'd rather not.

Marks
Greater Mark of Desolation
Greater Mark of Strength

Just some extra early game damage pushing.

Seals
Greater Seal of Replenishment

Early game mana regen.

Glyphs
Greater Glyph of Replenishment

More early game mana regen.

Quintessences
Greater Quintessence of Desolation
Greater Quintessence of Strength
Greater Quintessence of Fortitude

Either push for more damage or have some more health for a better early game.

Exhaust and Ghost Walk are the bread and butter of tankyDPS. Both can be used for both chasing and escaping.

Substitutes
Flash: Replacement for Ghost Walk. I find Ghost Walk better in the long run.
Ignite: Replacement for Exhaust. Score that last kill. I prefer Exhaust for more potential damage.
Teleport: Go where you please. Not one I would choose, but it's there.

The final build should be:

Frozen Mallet
Mercury Treads
Banshee's Veil
Atma's Impaler
Warmog's Armor
Infinity Edge

You should end up with about:

4500 Health
140 Armor
130 Magic Resistance
300 Attack Damage
Slow on hit
Block one negative spell every 45 seconds
35% CC reduction

It's a very solid build in my opinion. It lets you initiate while being able to take in a ton of damage and at the same time deal a good amount to enemy champions.

Build process:

Start off with a Long Sword and a Health Potion.
Buy a Phage.
Buy Mercury Treads, starting with Boots of Speed if you don't have enough Gold.
Buy the components for Catalyst of the Protector. Then buy Negatron Cloak. Ultimately finish Banshee's Veil.
Build Atma's Impaler, starting with Chain Vest if need be.
Build Frozen Mallet.
Build Warmogs.
Build Infinite Edge.

I start with Long Sword and a Health Potion instead of a Health Crystal because the extra damage pushes for a higher probability of scoring a kill. Phage is meant to give you more bulk and damage, along with more early game utility when you're trying to pound on enemy champions. Mercury Treads is standard for the Magic Resistance, Movement Speed, and CC reduction. Having Banshee's Veil as the third item makes your Mana management more flexible and at the same time makes you more bulky. Atma's Impaler is for the Armor and Damage compliment. Warmog's is for more bulk and damage. Infinite Edge is for the damage.

Of course, this item build is meant to combat balanced AP-AD teams. Here are available substitutes to combat against such teams.

AD-Heavy:

Mercury Treads vs Ninja Tabi
If they aren't CC-heavy, go for Ninja Tabi. Otherwise, keep Mercury Treads.

Randuin's Omen over Banshee's Veil
Armor instead of Magic Resistance, attack speed slow, movement speed slow.

Thornmail over Infinite Edge
Probably should build this earlier. Fit this wherever.

AP-Heavy:

Force of Nature over Infinite Edge
Deal less damage, move faster and take less damage. Seems like a good trade-off to me.

Jarvan can perform well in all lanes, but to my experience he's best on a side lane, preferably with a partner.

Early Game

You start with your Demacian Standard for the mini-ward it provides for the bushes in your lane. Use it constantly to avoid getting ganked or reveal potent targets.

You are a master of guerrilla warfare. Gain and maintain control of the bushes in your lane. Constantly harass with your E and Q, and when you see a ripe opportunity, E + Q knock-up a low-health champion, pop your Exhaust and Ghost Walk, and kill said target. Don't overextend, but be aggressive. Mind your mana, too. Moderate your skill usage. Take the turret in your lane down as fast as possible.

Mid Game

My definition of Mid Game on this character is when either your or your opponent's turret is down. At this point, you offer ganks and support to other lanes. CC, take down, push turrets. If teamfights arise, you're the man. E + Q to initiate, W to minimize damage and slow, R to trap, separate, whatever.

Late Game

Initiate, knock-up, shield and slow, Ult, team mates come in, hit, hit, hit, hit, die, "Ace! An enemy has been slain! Your team has destroyed a turret! Your team has destroyed a turret! VICTORY!"

I'll probably spruce up the guide to make it look better later, but at this point the content is done. Remember that one game does not make this a good or bad build. Please rate and comment.

As for the words of wisdom:

Teammates before enemies. Reason before ******ation.

Hope you have fun. :D