Jarvan IV has been my favorite champion in League from the day he was released. Why? He balances being Tanky and DPS...y better than anyone I've seen. He does crazy damage and has crazy health. He has a few drawbacks, but for the most part he is a very balanced champion and I can't play him enough.
Now, I'm not going to pretend this is a perfect guide, but it's something that has served me quite well. I want Jarvan to get more play time so I hope this helps!
Also, there are a LOT of good guides on this site so look around and feel free to blend some!

Pros:

• He balances Offense and Defense quite nicely
• He costs 4800 ip so you can afford him, but you won't see him against you very often
• He'll initiate a fight, do a great deal of damage, and walk out nearly unscathed.

Cons:

• He doesn't fill the Tank role and certainly not the DPS role perfectly. Only use him if both those roles have been filled.
• He's pretty slow. Speedy mage characters will probably laugh as they lob spells at you.
• Messing up the ult is a good way to get aced.

Here's the big scary secret about League: Masteries and Runes won't amount to much late game. Early game, they're very important, but later on they fizzle out. Granted, often times early game will determine your late game, but that's not my point. My point is that it's the items you get that set you and your opponents apart. How do you get items? Kill things. How do you do that? Level-up quickly. How do you do THAT? Stay in lane! Staying in lane longer will give you more options when you go back to buy items and it'll keep you ahead of your opponents who go back frequently. That being said, I tried to gear my items towards that end.

The main goal of these items is twofold: Keep you in lane, and balance Jarvan's Tank side and his DPS side.

: Gives you more damage than your opponents and the life steal will keep you in lane long enough to get an early lead
Mercury Treads : Jarvan is an initiator. That's what he does. You can't do that if you take one step out and spend the rest of the fight stunned. Even with the inclusion of the new tenacity items, this remains key to Jarvan's build.
Philosopher's Stone : Again, the mana and health regen keep you in lane longer. Plus, the bonus gold will stack with that, allowing you to buy the more expensive items.
: This item is pretty straight forward. Jarvan isn't the fastest fighter so he slows people to keep them close (that's why he has a slow, a knock up, and a trap). The bonus health and attack damage really define him as a Tanky DPS.
: Originally, I put this as , but Jarvan really doesn't have much magic resist. Banshee's Veil will balance out the bonus armor for his abilities and the next item, the bonus health and mana are a great asset, and the passive ability really helps initiate.
: Yes, yes, yes, and yes. Make sure you buy this. This item is perfect for Jarvan because it takes his already high HP and converts it into AD. That's exactly what makes Jarvan a force to be reckoned with.
: I'll be impressed if your game lasts this long, but if it does I recommend this item (sell your Doran's Blade for this one, by the way). It's an Infinity Edge, if you don't know what that means, you haven't played enough.
: Insert Crown and Prince joke here. Seriously, I didn't notice that until a few days ago. Anyway, the bonus cool downs and health are great, especially late game when you're not worried about mana anymore, and the active helps. By this point, you've purchased everything so the bonus gold is irrelevant and it's time to move on.

• First off you want to constantly drop your standard and shield . That's the whole reason for the cool down reduction!
• When you're attacking a tower, drop the standard on the enemy minions as quickly as possible. If they're not there yet, just drop it anyway. The attack speed will help you out. If you get the turret low and your opponents show up, you have to make a judgement call. Either drop the standard and your shield to take the tower out (a tower is worth one death, but one death only!) or just run.
• For the love of ****, do not use your ult on an enemy next to your teammate. I've done this a couple of times and it's been done to me a great deal more. Your teammate aren't made of steel and they need to run. Make sure you wait until they're clear. If you're ganking and you want to trap a wounded character with your whole team, go for it!
• Remember, you can use your ult to stop enemies from killing your team. If you see a group, trap them as quickly as possible with , then use your shield to slow them, and finally use your combo + to escape and run.
• Be very careful about using it on opponents with Flash or some ability that'll get them out. Try to make them burn it first, then hit them.
• Last word of advice about the ult: be weary of Vlad Vladimir. If he does his blood pool and you're in the air, the game will glitch up and it probably won't end nicely. Nothing you can do to avoid this, just don't use it on him during a team fight. One one one, it's fine, but never in a team fight.

This combo should be your bread and butter. Here's a few interesting things I've found can really make a difference and you might not expect just from looking at them.

• To pull the combo off almost instantaneously, you follow these steps. Hit E and drop the standard as close to the edge of your range as possible. RIGHT AS YOU CLICK TO DROP IT, hit Q , and click again. If you haven't moved your cursor, they should be lined up perfectly. The animation for Demacian Standard will play as you engage your Dragon Strike and you'll be pulled right to it.
• You can use this to get through walls. The offensive use very fun and extremely powerful. Do the combo through a wall and drop Cataclysm as soon as you appear. Your opponents won't know what hit them!
• Defensively, you can do the same thing to escape. Get close to a wall while your opponents are chasing you and use the combo to slide through. You can repeat if your cool downs are low, but be very careful because you could run out of mana and find yourself in a bind.
• You can engage a team fight (or any fight really) with this very nicely. Drop the standard either on your opponents or right behind them and rush to it to knock up as many as possible. The reduced armor they take and the time spent in the air should give your teammates the edge and ample time to gank.
• At the end of a fight, it might seem like an opponent is getting away. If you've maxed your Demacian standard first, the initial drop will do a good amount of damage. You can even turret dive by hitting them with the combo and using Golden Aegis to escape the turret blasts.
• The combo can let you escape team fights if they go badly. You can use it to first rush out and start running. Then, you can use it to put some distance between you and your opponents. Note that this second part only works if you're doing it instantaneously like the first bullet of this section.

Like I said, Jarvan is very balanced. He can walk in, smack some enemies down and walk out like nothing happened. Easy and simple. I'm still kind of tinkering with his build so if you have suggestions, I'd love to hear them! (But please be nice about it) In the mean time, get out there and "TOPPLE THEIR FORCES" D:< (or something clever like that)