Welcome to my very first build ever made =D I'll now explain how I play Jarvan, and what IN MY OPINION is the best way to play him. Jarvan is the newest hero released within the League, and damn he is good. If played well most of your games will already be over before u can get ur 5th item cause either they all rageleave or surrender, or you just pwned their base. I like to play him as a dps char who can take a bit of punishmet. I'll now explain why I have chosen this build, and why you should chose it!

DEMACIAAAAAA!

I take mostly armor penetration runes. The reason for that is that you will deal a huge amount of damage to everyone, even their tanks. Armor pen in combination with his Dragon strike(lowers targets armor for a couple of seconds) is deadly to even the tanks!
Next I have mana regen runes, cause Jarvan is a bit mana hungry, especially early game, so you need more mana regen to keep spamming your Dragon Strike. I also have CD reduction runes to let you even spam more of your skills!

For Masteries I take standard 21/0/9 masteries with more mana regen and max mana with ghost in utility. This way you are more leaning to the DPS side of your char, and you need that mana!

For summoner spells I take:
Flash: Overall I think the best summoner spell a melee dps char can have, and since Jarvan doesn't have the best escape mechanism this is your get of of ganks spell. It also lets you make that last hit if someone was lucky enough to flee from you. I say this is a must have!
Ghost: Your 2nd summoner spell can be alot spells. I take ghost since Jarvan is a slow char I want that extra movement speed. With the new patch minions deal way more damage to your towers, so lane control is now way more important. This lets you move faster across the map, getting to the lane you need to defend or just help your team gank. Also this helps you escape

Other picks
Exhaust: Exhaust slows the enemy champion so you can deal some extra hits. I would recommend losing your point in improved ghost and then putting it in Cripple, to make your exhaust more usefull
Teleport: I already explaind Jarvan is a slow champion, so teleport will get you to your destenation even faster! But the downside of this is that you cant use it as an escape mechanism, so its your choice to choose between ghost and Teleport
Cleanse: Helps you to get out of ganks when the enemy has lots of stunners etc. Also helps when chasing a char that when he stuns or slows you, you can still make that last hit and penetrate his body with your spear!

I start of withand 5xSince jarvan deals a fair amount of damage early game you dont need damaging items like dorans blade or something. I take cloth armor so I take less physical damage and since I go for madreds, I choose armor above damage, since you already deal enough damage. The 5 health pots lets me keep longer in the lane and keep my health up for my E-Q combo and get a couple of kills before teleporting back. Most of the times when I teleport back at lvl 6-7, depends on if I still got pots or not, I already got enough money for. If not getand another. For boots I take. This reduces the time of slows, snares, stuns etc which is great for Jarvan. I already explained that Jarvan is mana hungry since you will be spamming some skills. But Jarvan also needs attack damage, so for that reason I take. Gives attack damage and mana, and his passive's are great. Since you will be spamming skills you will quickly reach the bonus cap of 1000 mana that you'll get from it, and his other passive lets you deal even more damage, especially when you reached the mana bonus cap. Now we need some defensive items. Cause of his Golden Aegis's passive, you already got bonus armor, so now you need magic resist. For that reason I takeGives you magic resist, some bonus mana and health and it blocks one negativ spell cast on you every 30 sec! How great is that? Most of my games had been already ended by now, but if not this is the item you want:Gives more damage and gives 40% armor pen, so you will take down those heavenly armor tanks down in no time. Last I takefor more magic resist and increased survivability. If the enemy's are mostly physical attackers(like tryndamere or xin) takeinstead of

(passive): Some say this passive is quite OP, especially when used well. When attacking 1 target, every 6 sec you will deal bonus damage, 10% of their CURRENT health to be exactly. So when you're in a big teamfight try to switch targets so you will max out your damage.
(Q): Jarvan's main ability. He extends his lance dealing damage to everyone in the line of his attack, and lowering their armor for a few seconds. Early game this will be your harass skill and late game be sure to hit more targets at once, cause of the armor reduction. Also this is one of the key skills for his E-Q combo, but i'll explain that later.
(W): Jarvan's surrounds himself with a shield that absorbs a portion of damage, and it slows surrounding enemy's. If your health drops below 300 it's triggered automaticly, if its not on CD. This is the underestimated skill of Jarvan. I must say, the shield is kinda meh, but its the slow you want. Since you will not have slow items and not take red buff every time, the slow he has is very handy in every fight!
(E): This skills grants you passively more attack speed and armor, which is nice, and he can also throw the flag, damaging surrounding enemy's and granting the passive to other chars. This means you double you're passive! This can also be used to ward bushes if you think you're about to get ganked. This is the other key skill to your E-Q combo.
(R)(Ultimate): Jarvan's ultimate can be, when used right, a quite OP skill. But used wrong everyone will hate you. He jumps at a target dealing damage and makes terrain impassible around the impact, but you can still flash out and in, charge out and in etc. You need to know when to use this skill, you can't just jump at an enemy. You can trap yourself with every enemy, or trap your tank who is almost dead, let your whole melee team out of the fight and get yourself killed etc. You need to use this on lone champions, champions who try to escape, champions who are almost dead and you dont want to get killstealed:P Try using your brains when u want to use this skill. But still the keyword for this skill is Learning and gaining Experience on how to use it

DS =GA =DE =CA =
I start of with one point in DS. Use this skill quite often early game on the enemy, together with one physical attack (bonus damage cause of your passive) and you can harass quite good. Don't spam it yet cause you need the mana on lvl 2 to use your fearsome E-Q combo.
Once you hit level 2 put a point in DE and the pwnage can begin. If done good, you harassed the enemy, got enough mana and health cause of your health pots. Target your victim so your partner knows that to do. Throw DE BEHIND the target and then quickly use your DS THROUGH the hero and IN THE DIRECTION OF your flag. This will pull you to your flag and knocking up enemy's who where in the line of attack and slowing them. Now you already did a fair amount of damage. Now you are behind the target so you got a bit more time to hit him cause he is also slowed. Now auto attack him to the death togther with your partner. Your first auto-attack will also deal bonus damage, so getting a kill should be easy.
After u get youryou can start spamming DS and spamming your combo. Use the shield to slow the enemy's to land a couple of more attacks and use your ultimate on the right time.

Early game: Jarvan can already get 2-3 kills in early game, IF you keep your health up with the health pots and using your skills on the right way. You want to harass 1 champ and tell your partner to do the same. Watch your mana and dont play to agressively yet. Once you hit level 2 you can harass a bit more and then use your fearsome combo to finish the champion of. Don't get overconfident by attacking the other champion to, unless your sure you will lend a double kill. Keep playing like this till lvl 6-7, thats when you will teleport back and buy some items

Mid game: You now got lifesteal, which keeps you longer in lane and you deal some more damage. Keep pushing your lane, harass the enemy, lend a couple of kills if u can and gank. Cause of your combo AND ulti(if used in the right way) you can easily gank mid with your mid lane partner and get an extra kill or assist.

Late game: Now you got Manamune and a huge amount of mana, you can now start spamming skills and deal great amounts of damage. You want to be the 2nd to initiate in a fight, right after your tank. The best way is to initiate a fight using your combo. By now some of the enemy's got tired of getting killed all the time when they couldn't do anything to you. Some may have already rageleaved or started surrendering. If not keep pwning all the lanes and killing heroes, and the game should be yours:)

This is how I play Jarvan and it works for me. Just give me some constructive criticism and positive and or negative feedback. I already said that this was my way to play him, so if you find anything wrong or have any comments dont ragevote. Just tell me:)