This guide will help you to generally understand the role and tasks of Jarvan IV Support. I will emphasize on aggressive lane support, as I feel this is the highest time spike for Jarvan IV in bot lane. And then transiting to Engager Jarvan IV with some peel.

The outline:

Items. Example Build. Situational items explained.

Materies. Preffered Mastery shown, secondary masteries discussed.
Match-ups. Both for Ally and Enemy, given in 2 charts.
Lanining, Aggressive play is described, Shown, and cases explained.
Section for Updates. Some answers on questions, new knowledge.

I pretty much said everyting I wanted in notes, except you might want to know I don't buy Boots and Sightstone. As for boots you have a quick gasp closer to reach short distances quicky, plus I find that boots bring the constraint to tankiness, as the defenitely give less stats than other tanky items like Frozen Heart. I don't buy sightstone, as ideally you should win or at least strongly dominate the game in Mid and Early stage, given this you shouldn't be afraid of enemy map movements ,as long as you watch the map and ward nearby. However if you are not doing well, while one of your carrying teammates asks you to buy sightstone, I advise you to do it to make his play more comfortable.

There are 2 item you may consider. locked of the iron solari. This is essential to buy if you have high AOE AP enemies like e.t.c
You can consider [Redemption] if you fall far behind and lost your lane. If it happened you don't get enough farm to get tanky soon, so [Redemption] will help you to bring more utility. However the reason why I don't build this item ,is because I play as an engager and try to take all the damage on myself. Using E Q and active shielding items to peel for squishies.

Another option I very rarely build is going AD. You can consider it, if all your lanes are winning and consequently no enemies are fed. This may help you to end the game quicker by eliminating enemies faster and having more push power.

I want to point that I didn't do any calculations, my build is based on my experience only.

There are 2 options for Jarvan support. If you have a mobile adc chapions in enemy team like e.t.c you need to pick Exhaust, so their mobility is reduced and if the go into your adc they are less effective.
Otherwise pick Ignite This can help to secure the kill and have a vision of escaping enemies who go into bushes. Make sure however that you if you are fighting and have an advantage you use it so the adc takes more damage, receives less heal and cannot hide in bushes.

However if you play normal blind ,it is more reliable to get Exhaust ,as you don't know enemy pick and it can be put in good use anyway.

The main role of Jarvan IV during lane phase is to get your adc fed. This what really makes him outstanding as a support. He can go in as ,but deals way more damage. You want to make sure you are good with EQ combo, as if you screw this up you will get nothing but some shots in your face, if not death. If you don't CC just go back asap. Make sure your adc follows your aggro, otherwise you fighting 1x2. In most cases you don't want your adc to follow if your EQ was unsuccesful.
You should start going in once you hit 2 level and get E Q, however if you are not sure about going in, wait for 3 level to get W.
After you CC with EQ make sure you do at least 1 AA to get passive proced. Don't use your W immediately. If your enemies are running away let them run, unless you and your adc can chase them and kill, in that case use W to slow them.

You want to fight and give kills to your adc, so make sure lane isn't pushed to their tower, otherwise you get nothing but both sides farming and you standing at risk of ganking. The only situations you want your lane to be pushed to enemy tower Is 1) if your enemies Max 50% HP and your Jungler is ready to dive. 2) You enemies low HP and you and your adc have high chances to kill them/one without dying. I don't know if I have to mention it but be careful with diving Caitlyn ,high chances dive especially 2x1 2x2 won't be successful and can be deadly.

The are mainly 2 conditions , when you can roam/scout:
1) You just killed enemy bot and you have enough HP to roam.
2) Your adc is able to stand alone in lane. Usually if your adc is fed enough he can stand alone, or if your adc is smart enough to farm 1x2. But just make sure to ask your adc not to push the lane if you feel he can do it. Always watch your adc while roaming, if he is in danger come back ASAP.

Resons to roam: (or what you should get from roam)
Put pressure the rest enemy team
Burn flashes ,mainly with EQ or R
Kills/Assists
Get your jungles fed.

If the mentioned criteria is met feel free to roam.

In this phase your role is to engage. Needless to say that you have to make sure your engage can be followed and your engage will most likely bring the win in teamfight.
The highest Engage combo works with and
As their R has crazy synergy with yours.
Note if your adc is fed you also want to make sure he has at least decent condition to deal damage as if he gets eliminated quikcly all your work during lane phase is wasted. Make sure to have your Knight's Vow on him and use Face of the Mountain. Also EQ everybody who tries to tries to get him out of teamfight. So if enemy melee keeps going into your

I am still working on this guide.
What you will see soon is completed match up both for enemy and ally team; visualized items, comleted outline.
I may also see videos soon, but only if I will manage to get this videos working
If you have any question or suggestions leave the comment and I wil try to cooperate and incorporate viable questions and issues in the guide
I will also try to add more theory to make you understand and learn more about Jarvan support.