I've played a lot of Jarvan top and all I can say is that he doesn't excel as a damage deal as much as we would like. Sure, he has a nice burst from E+Q+Auto+Ultimate, but that's where J4's damage ends.
Attack speed build is a very innovative thing on him. His Q scales 1.2 from bonus AD which is actually a good scaling, but after your Q is done there is only one AD ability left: Your Ultimate. So basically all your AD abilities are a 4-5 seconds CD Q and a one-time teamfight ultimate...and that's bad.
But Jarvan 4 has an ace in the hole. His little flag which passively increases his attack speed by 22% at max rank, further increasing by 22% more when activated, so a total of 44% attack speed - which is great!
So I choose this build because it is sustained by J4's attack speed ability and because moderate-heavy AD just doesn't work on him - he is not Pantheon after all!

I usually start with Corrupting Potion for that additional mana and its burning effect.
You can also start with Long Sword and 3 health potions but keep in mind that your mana won't have that much regeneration.
If you choose Long Sword your damage will obviously be bigger but you will lack some mana regeneration.

1. Harassing:
- You will try to harass with Q as much as you can, but keep in mind your passive. Your passive is an excellent damage dealer and can make the difference between the trades with your opponent.
- At level 2 you should pick E because it can be both an initiator or an escape, also it gives you attack speed boost wich helps the early damage tradings.
- At level 3 you can make use of your shield not for direct combat, but for harassing. Approach the enemy and make use of your passive, striking him for one or two melee attacks. Right when the enemy wants to riposte use your shield to slow him and absorb some of his damage and his minion's damage. Right when the enemy finally decides to retreat from the trade, use your Q as a last harassment tool.
- You should never use E unless you actually want to initiate on your enemy. Keep it for potentially escapes.

***THAT's ALL FOLKS***
I won't bore you with additional details. You have to try the champion yourself, test the build and you will find what matchups are harder and which one are easier. I guess we can all agree that a Nasus or Renekton are almost impossible to defeat, that's why I won't bore you with additional boring stuff that might give the impression of a "detailed and professional guide". You have the items, you have the reason why, now go on the Fields of Justice and try it out!!!