This is the way I like to play Jarvan. It isn't perfect, so if you have any suggestions please feel free to tell me. Also, this is my first guide so I am not sure how to put the item's pictures in here, so if you can tell me that too it would be appreciated.

Pros:

Kind of tanky throughout the whole game
Can dish out lots of damage with this build late game
If the enemy doesn't have flash or a good escape mechanic can ensure a kill
Can trap an enemy dps or carry away from the teamfight for a few seconds if you do his ulti well
Great Initiator


Cons:

Can sometimes trap a teammate in his ulti
Doesn't do a lot of damage early game with this build
Is susceptible to magic damage, but the health sort of counteracts this

I choose Marks of Desolation because end game you want that damage, and early game it helps you get that first blood.

Seals of Fortitude because it helps survivability and we are going to be grabbing an Atma's.

Glyphs of Focus since his W and E cooldowns, as well as his ulti, is kind of long and it makes them more spammable.

Quintessences of Desolation for the same reason as marks.

I go 9/21/0 since you get much more survivability, which you will want late game, and so you get just a bit more armor pen as well as cooldown reduction.

The Wriggle's Lantern helps you be a little more tanky as well as give damage, lifesteal, and helps you farm. The ward is just a bonus.

Ionian Boots of Lucidity for even more cooldown reduction that you might need, but feel free to grab Merc's Treads if they have high cc, or if they have an all AD team Ninja Tabi is fine.

Last Whisper for the extra damage and it helps if they get some armor.

Warmog's for more survivability and to increase your damage on Atma's when you get it.

Atma's because if you get to Frozen Mallet you have over 4,000 hp and it helps bring in a lot of damage on top of its extra armor.

Frozen mallet since you might need that ace and don't want anybody to run, as well as a bit of extra damage and more hp for your Atma's and survivability. If you are having problems with magic damage (I'm not sure how because you will have over 4k life) then grab a Banshee's Veil instead.

I go R>Q>E>W because you need the damage and armor reduction your Q gives you more than anything else. Feel free to get E first if you want, but I dont recommend it.

I take exhaust just in case they live when your ulti goes down and it doesn't let them run. Ghost for the same reason. Exhaust also helps if you are about to die and need to get away as well as killing someone with very high damage.

Other spells you might want to take would be Ignite or Flash. I don't really think the rest are needed but it is all up to preference.

So like I said, this is how I play him personally but you can always change it and tell me how I can make this build better.