Jarvan is a great hero. I have seen many people trying to build him as a tank/support champion and in my opinion this is the wrong way to play Jarvan. He is a durable DPS that can put out a ton of damage if you build him the right way while still being incredibly durable. This build aims to maximize his strengths and minimize his weaknesses.

Q: Dragon Strike - This is your main DPS nuke, it has good range and hits multiple targets. Very effective at poking due to its deceptively long range.

W: Golden Aegis - Shield that scales with the number of enemies present and slows in a small AOE. Always use this when escaping, initiating or chasing.

E: Demacian Standard - Provides a passive bonus as well as an active bonus to nearby allies, deals negligible damage in a small AOE. Can be used to gain vision in bushes or fog.

R: Cataclysm - Great initiation move that deals decent damage and traps enemies in a impassable ring for a set time. Great against enemies without flash or a dash type move. Can single handedly decide team fights if used properly.

Start off first with a long sword and a potion. The reason for this is that you want to rush a Sword of the Occult as soon as possible as Jarvan is great at pulling of kills in the early laning phase. SotC is the heart of this build as it uses Jarvans ability to get KB's as well as his ability to escape deaths to quickly build stacks.

Next get whatever boots fit best against the team you are playing. For me it usually ends up being Mercury Treads for the CC reduction.

The brutalizer is the next item you will want. The cooldown reduction and armor penetration will allow your Q to do a lot of damage.

Now we start building for survivability as the team fights are going to start coming.

Get a catalyst and build into a Banshee's veil.

Now we get a Warmog's Armor, I know a lot of people don't like Warmogs and prefer to buy resistance items but Warmogs is crucial because it allows our next item to be very effective.

After the huge HP boost from Warmog's get an Atma's Impaler, with your large HP pool it will add a great deal of attack damage as well as the armor and crit.

Only after you have bought all these things upgrade your brutalizer into a Youmuu's Ghostblade

This item build keeps Jarvan effective all through the game, meeting his immediate needs at each phase in the game. Near the end if you have kept your stacks and have your Atma's you will be very hard to kill as well as putting out damage the equivalent of other all DPS item builds.

I think it is important to Max Dragonstrike quickly as it is your main nuke and will clearly be the highest source of your damage.

You want one point in Demacian Standard early so you can hookshot.

However I think that points are better spent in Golden Aegis for the survivability and slow for chasing.

As with most champions it is best to put points in your ult when you can.

The most iconic move in Jarvan's arsenal is what I call the hookshot. As I am sure you are aware this is performed by placing Jarvan's standard and aiming your dragon strike at it pulling you to the flag and knocking up enemies along the way.

A couple useful facts about this technique are that you can shoot the dragonstrike before the flag animation completes and you will still be pulled to it when it lands. This gives you a tiny boost in chases and escapes as well as an element of surprise when initiating. Another thing to note is that the range you can hookshot is a tiny bit larger than the range shown on the dragon strike reticule, this means you can hookshot to a flag that looks a tiny bit out of reach.

This is an important initiation tool, a chasing tool, as well as an escape tool in conjuction with your Golden Aegis' slow.

Whenever chasing or running remember that it can be used to pull you over ledges, even ones with fog on the other side because the flag gives you vision. This is especially effective along the river in summoner's rift and in twisted treeline.

When you see a teamfight coming start planning out how you are going to use your cataclysm. You want to trap squishies in but leave powerful melee DPS out. Always be looking for opportunities where you can make this happen. Tell allies to be ready to use ranged attacks to nuke the people you have trapped. If you trap more than you can handle and are being killed by melee, golden aegis then hookshot out of the ring.

Ghost
Exhaust

These are my preferred Melee DPS summoner spells, however it is always up to personal preference, take whatever spells you want.

Early in the game do your best to last hit while staying at a safe distance from your enemies, use your Q to poke at enemies and keep them from farming freely. When you've got your E>Q combo you are ready to start ganking, make sure to communicate with your partner when you are going to hookshot into the enemies as this can easily result in you being ganked if you go in without assistance.

Always remember to check bushes with your flag when possible, it gives you vision.

In team fights you should always initiate but make sure your team is right behind you. When the CD is off it is best to Cataclysm to initiate. However when it is on CD E>Q works great as an initiation move.

Your E>Q and W make you an excellent chaser but be sure to know your limitations.