After clearing your buffs, try to gank the lane that will most likely will give a kill to your team.
Enemies with their flash on cooldown are ideal targets after you get your ulti.
As the game goes on, you will be dealing way less damage but you will be the tankier one.
Thus it will be your role to start teamfights. Be careful in choosing the place, the time and the way of your engagement properly in a way that benefits your team.
Tips & Tricks
Αsk for your teammates to provide a smiteless leash for your fist buff.
After that you can easily grab your second buff with smite and look for ganks as you will be level 3.
Always communicate with your teammates as to where enemy wards are so you can choose the best ganking path.
Don't be hasty in using your cooldowns, pick the proper moment.
Try to get as many of your enemies inside your ulti.
CAREFULL! Try to not trap a teammate who would rather not be there inside.
Remember, if you reactivate your ulti, the wall will go down.
Jarvan will work fine with any AoE team comp as his ulti can keep opponents in place for quite a while.
Avoid picking him versus compositions with lots of escapes and blinks, like Ezreal, Kassadin, Renekton etc.
In the jungle Lee Sin and Shen are your worst opponents. They will both beat you up if they catch you in their own jungle so avoid counterjungling and try ganking more.