As a jungler you should be doing one thing from the moment the game starts: gathering information. You are the man behind the curtain for the bulk of the game, and you need to be one step ahead of their team to have the greatest effect on the outcome.
You should be watching the minimap constantly, always ready to ping information for your teammates and to see if their jungler pops up. Make sure to find out where their jungler started, counter-jungle if you play a jungler who can duel.
While taking your 2nd buff tell your teammates to care for a gank. If they started at bottom buff, tell top/mid to be careful. They'll usually take the hint and use their yellow trinket at this point. If one of your lanes is pushed, you can bet the other jungler will be ganking any time. I usually tell that lane that I'm going to go for a counter gank and position myself for an easy interception of their incoming jungler. It's pretty rare you lose a 2v2 if you have the element of surprise, so counter-ganking is usually a great idea. But you need to know what the other jungler is thinking. This early in the game it's obvious, later on you really need to be paying attention or warding extremely well.
Some other ideas/reinforcements of nonfiction's sound advice:
- Diligently record buff timers, even late game so it becomes automatic
- Ward early and often, swap yellow trinket to red on first or second back.
- Ask your team to communicate with you as much as possible about summoner spells and ward placements. Knowing is >50% of the battle, imo.
- Don't be afraid to be test the limits of your champ, and own up to overextensions quickly to keep your team on your side.
- Learn to buy your starting items while moving to the nexus, and rush their jungle for an easy first blood. (When my game loads I instantly move to the side of the nexus where I can still shop from, press P, buy things with right-click, ESC, spam "trundle is on his way" pings to a brush in their jungle.) The higher level I attain the more people I see out of base in under 15 seconds, you can get summoners or first blood with 3 people depending on champs.
- Learn to mute people very early if they are abusive towards you as jungle or just don't understand that there are 3 lanes, not just one. If you remember you can unmute later when they cooled off and you need to communicate.
- Use travel time to communicate
- Rush jungle item, sometime before boots if all lanes are even!
- Ward their starting buff and surrounding area at 6:40, even if you don't steal your dumb teammates will mobilize for a counter-attack to the gank that usually happens after.
- Get good at checking your smite damage and maximizing your burst when taking buffs.
- If you expose yourself to the enemy team, make sure it's for a good reason. Just the information that you are bot lane for a split second can affect the decisions their team makes. Think about what you are telling the other team every time you show yourself.
- Play Trundle if possible