Item Build

Starting Items

Starting items really depend upon players, but the selection of pots and wards is the most up-to-date one in Season 3. As a Jarvan player, you must remember that he has no sustain. So it becomes more difficult if the enemy brings pots in level1. To go against them without any problem, preparing pots seems the most appropriate. Buying wards is a must when you bring a lot of potions. Without ward(s), you can die even before using all your pots by ganks. Plus, make sure you use all the pots before dying or there is no point to bring pots.

Core Items

VER 1: Against AD champion at Top

The key point here is building Warmog ASAP. However, building armor items is fine when you are losing your lane (try Chain Vest or Doran's Shield against strong early game bruiser champions such as Pantheon or Renekton). Brutalizer(or Blackcleaver) is now a general item for AD bruiser at Top. With the unique passive and Jarvan's Dragon Strike, Jarvan can survive and continue to farm at top (or obtaining a kill with a gank). Increasing health with these items is very important to take the damages in the teamfight (but also remember you will get damage if and only if you are a threat to the enemy team's ADC or Mid AP champion).

VER 2: Against AP Champion at Top

Hexdrinker is a very nice item to win the Top lane. But, you sometimes need to get a Brutalizer first because the AP champions at Top will build Arm Guard as soon as they possible. Without Brutalizer, your skill/auto-attack cannot hurt the enemy champion (Especially Jarvan IV without sustain will be in trouble). Once you get Warmog, you can take a lot of damage and still can survive in teamfights. The build can be changed as how the games goes, so plan smart (try many new items in normal games in order to plan).

Endgame Items

My 6 item build would usually look like this. I personally believe Jarvan IV does not need much damage (different situation can come) to deal enough damage as a tanky DPS. Instead, increasing health is an important point and so building Warmog is very important (especially because the Giant Belt provides less HP than before). Depending upon the games (especially against two/three AP champions on the enemy team), it is recommended to get Hexdrinker or Runic Bulwark (which gives you a lot of Magic Resistance . Lastly, Trinity Force also works well with Jarvan IV (It used to be my main item in Season1 and 2).

The list for the situational items is pasted here from the main page (Order does not matter).

Adding some comments about the items above,
  Buidling Trinity Force / Mercurial Scimitar is a good way when Jarvan IV has a lot of kills and we have tank(s) other than Jarvan IV or Jarvan IV needs to kill the enemy team's carry champions. Mercurial Scimitar is especially good to assassinate champion(s) as nobody can stop Jarvan IV with the active ability.
  Thornmail can be really good item especially against all AD champions on the enemy team (I recommend to build it especially when you lost Top lane against Darius so you can take his ultimate damage in teamfights).
  Stinger is a very nice item that allows Jarvan's Auto-attack speed much faster than the enemy champion. I would recommend this against champions with high attack speeds (such as Jax/Xin Zhao).
  Tear of the Goddess is an item you must be careful to build. This allows you to play Jarvan IV like Jayce. By overcoming Jarvan IV's poor mana pool, he can spam his Dragon Strike skill just to poke the enemy champion and minions. ** (Warning: try out this item in normal games first) ** Buying Tears can make you behind in earning tanky items.
  Philosopher's a nice way to snowball at Top lane if you cannot win or there is no reason to fight at Top (It is not recommended against some champions that also focus on farming to be strong such as Jax/Irelia).
  Locket of the iron solari is not highly recommended, but can be useful as a tanky item to initiate a team fight.  
  Ruined King is so popular now due to a huge buff on the item. This item basically works well on every champion (even some AP champions try it just to get Vamp..) After some time in game, replacing Stinger with Ruined King would be a nice choice. With this item, Jarvan IV does not need more attack damage items.