Jarvan IV is a great tanky DPS champion who is fun to play. His awesome survivability combined with his skills' synergy and insane passive allows him to quickly win both solo and team fights. The rule of thumb I like to follow is 10 games with a champ before starting to figure out how to play them. Here is what I have found to work with him.

Pros
-Great at dealing damage quickly
-Can tank/off tank and engage
-Super AWESOME ulti...trapped lolwut?
-Skills and passive have good synergy

Cons
-Susceptible to early burst damage harass
-Ulti can work against the Team
-Can't solo carry QQ
-Long cooldown times

Masteries (Important Ones to Take)
Cripple: Make your Exhaust even better
Haste: Makes your Ghost more effective since you are a very slow champion

Summoner Spells to Take
Exhaust
Exhaust is one of the best spells to run on a tank. You can slow enemies for a kill, protect your carries from their carries/anti-carries, or slow them to run away. All around, it is just the best.

Ghost
Ghost is the other skill you should run on Jarvan IV. Since he is so slow until you pick up some movement speed, Ghost will let you chase or run effectively.

Situational Summoner Spells
Flash
If you are a Flash pro, then you can probably make this work (especially against those annoying champions with their own flash/built in flash). However, I prefer ghost because Jarvan IV is a slow champion and really benefits from the speed boost.
Ignite
If you would prefer a more offensive role or better lane dominance (or the have pesky healing characters like Soraka or Swain), run Ignite.
Telelport
If you prefer Teleport over Exhaust or Ghost, or you think you need it for a solo lane or such, go ahead and use it.
Cleanse
Cleanse is a great spell for melee DPS/tanky DPS/tanks, but I find the other two better options. However, if you prefer cleanse, then use it!
Heal
Heck if you can make this spell work, then by all means take it. (just seems like you have better options IMO)
Fortify
Even though you probably shouldn't be the one running this spell, sometimes circumstances call for sacrifice.

Runes to Take

9x Greater Mark of Desolation Greater Mark of Desolation
-Running these will allow to you to deal a ton of damage if you strike them
9x Greater Seal of Resilience
-Running these is important in making up for your lack of early game armor
9x Greater Glyph of Warding
-Running these is important in making up for your lack of early game magic resist
3x Greater Quintessence of Swiftness
-These will help you with your slowness early game, and since they scale off total movement speed, they get better as the game goes on.

These runes will increase your lane staying power while also giving you massive damage

Other Choices

9x
Greater Seal of Eveasion/Greater Seal of Fortitude
For increasing your dodge chances or adding more health to your small starting health pool
9x
Greater Glyph of Focus/Greater Glyph of Celerity
Cooldown reduction to spam your abilities even more, allowing you to better dominate the lane and support your team
3x Greater Quintessence of Desolation
Greater Quintessence of Fortitude/Greater Quintessence of Desolation
Also for more early game health (see seals above) or early game damage.

Jarvan is a great melee DPS offtank. As such, your goal in the lane is to maintain dominance from level 1. While this may not always be the case due to your lane opponents, such as Sona, the ultimate poker, you should strive to complement your lane partner or demolish your opponent.

First Two

Start with a Regrowth Pendant to complement your high starting mitigation (from runes and masteries). This will allow you to keep laning past most lane opponents. The Mana Potion is to allow you to counter-harass and stay in the lane, as in doing so you will deplete your small mana pool rather quickly.

Next Three
philosopher's stonephilosopher's stone
Mercury's Treads are needed on Jarvan IV since he is the engager. Turn Regrowth Pendant into a philosopher's stone, and get a second philoshoper's stone for the gold/10s and health and mana regeneration. Since you pack a high amount of mitigation already (from your runes, masteries, Mercury's Treads, and Demacian Standard passive), you can afford to go health and mana regeneration. Also, the mana regeneration will allow you to use your abilities far more often, enabling you to better support your team.

THE CORNERSTONE!

Why Trinity Force you ask? Well, for several important reasons.

1. You get health and mana
2. You get movement speed
3. You get a slow (even more CC!)
4. Most importantly, you get an awesome passive!

Start building Sheen first to help with your mana problems and to be able to hit hard after a well-used dash. After that, move on to Zeal for the movement speed since Jarvan IV is a very slow champion. Wrap up the combination with Phage, and then finish Trinity Force.

Tank Time

Now you are ready to move on to the tank items. I usually start with Warmog's Armor because with your tankiness mid game, I find it more effective to get health to expand your effective health instead of more mitigation. However, adapt the item order to your game. If they are magic heavy, work for Banshee's Veil first. If they are attack damage heavy, get Frozen Heart. Why no Sunfire Aegis or Randuin's Omen you ask? These items are more for your true tanks, who lack damage. Plus, Randuin's is not as viable as it once was due to the armor, health, and CD reduction nerfs. However, if the situation calls for it, you can always trade the Atma's Impaler for Randuin's Omen, Force of Nature, or Sunfire Aegis. In addition, I find that the 99 armor and 20% CD reduction from Frozen Heart is much more useful than the 450 health and 35 magic dmg/s from Sunfire or the 8% CD reduction, 75 armor, and 300 health from Randuin's Omen.

> > +

Martial Cadence
A great passive, it outputs a lot of damage early game and synergizes well with Trinity Force later. Use it to your advantage by autoattacking enemies as often as possible, preferably right after a Demacian Standard > Dragon Strike combo.

Dragon Strike
The very first ability to level. It is the cornerstone of the champion that is Jarvan IV. This is the ability that lets you perform all the roles of initiate tank, tanky DPS, and AD carry support. The 100% bonus attack damage scaling and high base damage means that Dragon Strike hits very hard even without an abundance of damage items or offensive masteries. In addition, the armor reduction portion of your ability makes your basic attacks and your team's basic attacks hit even harder, allowing your team to effectively shred the enemy champions' armor to nothing. Most importantly though, is the Demacian Standard > Dragon Strike knock-up dash combo. By leveling Dragon Strike, your combo, when landed, will deal massive damage to the enemy champion. It gives you the power needed to maintain lane dominance. Use the dash combination to start a team fight by knocking up most/all of the enemy team. Remember, this is your primary mode of CC, so spam it because one knock up could mean the difference between life and death for you or your teammate.
**You can also use it or the dash combo to farm creep, but that is discouraged until you have sufficient mana regeneration.

Demacian Standard
The second ability in your bread-and-butter combination. The armor and attack speed are a nice bonus, but you really don't need the bonuses due to the tankiness from your masteries and runes. As such, just get one level of Demacian Standard at level 2 and then move on to maxing Dragon Strike and Golden Aegis first. Using Demacian Standard will help you survive against attack damage laners such as Ashe, Vayne, or Corki. (especially when you use your combo to hit them and the bonus armor protects you) Remember to try not to unnecessarily spam Demacian Standard because it is mana intensive (and will strain your small mana pool), but use your dash combo whenever possible.

Golden Aegis
Start leveling at level 4. You need Demacian Standard at level 2 because you need Demacian Standard to use your dash combo. However, after the one point in Demacian Standard and maxing Dragon Strike, leveling Golden Aegis becomes your priority as you start team fighting and you need the survivability. Just as well, Golden Aegis becomes a very useful asset later in team fights, when you can use the passive to generate extra shield and perform a mass slow. When team fighting, make sure to spam this ability as often as possible to both slow any fleeing enemies, to protect yourself after an engage, and to get another Trinity Force proc.

Cataclysm
Probably Jarvan IV's most difficult skill to use properly. Make sure to level it whenever possible and always pay careful attention to situations to use it. You should follow these guidelines for using Cataclysm.

1. Whenever you are about to kill an enemy champion in your lane
2. The enemy is fleeing and you need to quickly close
3. Your team is coming to help/gank and you need to keep your opponent there
4. To start a team fight
5. To keep the enemy tanks/carries away in a team fight
6. To save your teammates
7. Most importantly, to hear Jarvan IV yell "DEMACIA!"

Remember, use Cataclysm at your discretion. If your teammates are yelling at you, you should probably listen to their complaints.
**Try to save using your Cataclysm after enemy champions use Flash or abilities such as Tumble, Shunpo, Riftwalk, or bushwhack/ pounce.

Starting Team fights and Using your Ultimate
Since you are a great engage tank, ENGAGE ENGAGE ENGAGE. Make sure to dash in to the enemy team to knock them all up and start the team fight, or Cataclysm to give your team a chance to catch up and start team fighting. (you can even dash into a Cataclysm if that is what it takes to hold the enemy team in place) Use Cataclysm at an appropriate time, such as to isolate carries at the beginning of the fight or to catch fleeing enemies. If you have teammates like Karthus or Miss Fortune, use your ult to hold enemy champions in place for Lay Waste or Bullet Time respectively. You can also use Cataclysm to hold enemies in tower range for a tower dive kill or to finish off enemies when they are low health.

Team Fighting
REMEMBER, it is OK to die! Your job is to use your Demacian Standard > Dragon Strike combination on CD to knock up the enemy team and do damage. The combo is especially useful to slow down the enemy team's tanks, protect your carries from their team (you can knock up champions mid ability such as Shen's Shadow Dash or Vayne's Tumble), or to jump to the enemy carries in the back to focus them. The dash will also activate Trinity Force's passive so you can deal some significant damage during the fight, but you should use dash to protect your carries instead of to deal damage if given the chance to use it multiple times. (that means knocking up their carries or tanks depending on your team's positioning) Just follow team fighting basics as Jarvan IV and you should do fine.