=-Lead the team-=
=-Help the lanes-=
=-Know everything that's going on on the minimap-=
=-Predict the opposing jungler-=
=-Ward the opposing jungle-=
=-Serve as a beacon of communication-=
=-Encourage the team-=
=-Secure Dragon and later on Baron-=
=-Secure own buffs-=
A jungler is the main core of the team. You are the one that is everywhere, so you must know everything. Your map awareness has to be excellent and your prediction skills have to be excellent and your leading abilities have to be excellent because if they are not and the enemy jungler is a tiny bit better than you at all of those then you will lose.
It is because of these reasons that a jungler can NEVER rage. Even if the team is yelling at you for their mistakes (which happens all the time;; top lane loses 1v1 firstblood "JUNGLER NOOB") you cannot rage. You have to understand the team's complaints and, if they were wrong explain what they were doing wrong and help them as much as possible. If you did make a mistake be the bigger man and apologize and straighten your mistakes.
Otherwise you will lose because everyone is too busy fighting to focus on the game.
Play to get better
Learn the junglers. Learn how much damage they can do, learn their range, overall clear time, etc. It is easier to jungle against a champion that you are familiar with.
Learn to lead
REMEMBER! A gank is successful as long as you at least make the opponent waste a summoner.
If I decide to counter-jungle or just ward, I will say in chat " Going enemy jungle please help if necessary! " They know what's going on, they know what will happen, everything's planned, there's no chaos, the match goes on in order.
Sometimes you will not have time to say it but that is OK because that is why pings exist. Teammates will notice multiple pings and try to help you unless they are blind or stupid.
By midgame you should be able to figure out how this game is going to turn out. If your teamcomp is not built for teamfighting and you know you will lose the game if you 5v5, say in the chat "We should not teamfight." This is communicating to your team.
Communicate to your team what you are going to do. Before a gank I will ping the lane and ask if there is any ward. If there is, I will try to either gank from another angle or go to another lane. If there is not, I will say "I gank" and gank the lane with my teammate.
1. Blue > 2. Wolves > 3. Wraiths > 4. Red > 5. Golems > 6. Wraiths > 7. Wolves
1. Red > Wraiths > Blue > Wight> Wolves > Wraiths > Golems
#Ganking after double buff:
1. Blue > 2. Wolves 3. Red > 4. Gank
1. Blue > 2. Wolves > 3. Ward enemy Red > 4. Take their golems >
5. Steal their red (smite) > 6. Kill enemy jungler or head to safe area > Base
-Blue buff: Initial spawn: 1:55 min, respawn time: 5 min.
-Red buff: Initial spawn: 1:55min, respawn time: 5 min.
-Dragon: Initial spawn: 2:30 min, respawn time: 6 min.
-Baron: Initial spawn: 15:00 min, respawn time: 7 min.
GREEN: Should be warded all the time.
PURPLE: Should be warded when you are doing Baron.
BROWN: Should be warded when you are doing Dragon.
RED: Agressive wards at enemy's buffs.
BLUE: Securing your own buffs.
Most of the times it will last very long.