Note after spending like a half hour typing this: this is long. There's a 3 sentence summary at the end that is nowhere near to as detailed as the full thing, however if you don't want all the juicy details of jungling in random, fragmented thoughts as I thought of them, go to the bottom and read the TLDR. However, if you really wanna be a jungler, I recommend reading the full thing.
Well, I could go in-depth with smiting strategies with the extremely unique and cool smite buffs, but they're about to remove those next patch. So, instead, there'll be a lot of new strategies popping up in the preseason, but smiting will basically be hold a charge any time you want to take dragon/baron, otherwise use them as you wish.
Instead, jungle monsters now give more exp, but have different strategies to beating them. The raptors will be awful for anyone who is single target focused, so ignore them if you are. Krugs will be awful for pretty much everyone. Kha'Zix will rule the jungle with his ability to take out now 3 camps with isolated Q, plus his changes are legit busted, so pretty much just play him and you'll be golden. Also, tanks with hard cc will be busted with the new keystone that's replacing Strength of the Ages, so play them and get free 5k health shields for ccing the enemy team.
Start at top side if you want to get off an early gank bot lane and bot side if you want to get off an early gank top lane. There are a few different clear types: full clear, buff secure, and level 6 rush. Full clears will end you out at level 5 now, and you basically just go Gromp -> Blue -> Wolves -> Raptors -> Red -> Krugs if you start at Gromp, or the other way around if you start at Krugs. with all camps now giving you a heal for smiting them, you don't have to adjust your clear if you're a low-sustain jungler to get the Krugs -> Raptors -> Red to give your smite time to recharge, but you still have the risk of being invaded by the enemy jungler if you don't, so make sure you ward up before doing red buff if you started red side. Buff secure clears have you doing your starting camp, nearest buff, then the other buff, and it's pretty much just to ensure that you don't get any of your camps stolen by the enemy jungler. Do this if it's someone you think will invade you and try to steal one of your buffs without running into you, like Nunu. Level 6 rush is pretty simply you do a full clear ignoring the buff camps, then do another full clear, this time getting the buff camps, and you end off at level 6 and have your buffs available to gank with. Do this with level 6 reliant junglers, like Warwick.
A few junglers have unique clears that only they have. For Nunu, he is the ultimate control jungler. I would start by warding over the wall at one of the enemy camps to see where the enemy jungler is starting, Krugs or Gromp, then go into the other side of their jungle and take that entire side. You will start at their opposite camp, but a point in your Q level 1, your W or E level 2 (it doesn't really matter too much, but W is a lot more mana efficient), and then another point in your Q level 3. Take their full side that they aren't starting at, starting with the closest camp to where they'll arrive when they get to that side (wolves or raptors) so that they don't show up in the middle of it (awkward situation if that happens), and then go to the buff camp and then the usual starting camp. Save your smite for the buff camp on red side or use it on the wolves on blue side, that vision is really useful from the wolf spirit. Though that won't be a thing anymore in a few weeks. From the end of the enemy jungle, gank a lane or go into your own jungle and do a full clear, or both. You're Nunu, you can literally stay out forever if you wanted. Just make sure to grab the scuttle on the way back to your jungle.
Shaco is another jungler with a unique clear. He will generally start at his buffs with no leash, start his W, and start throwing down the boxes every time they come off cd at the earliest possible time that he can and not have any expire by the time the camps spawn. From there, it's just a full clear.
Nidalee has another unique clear that is necessary to come out of the jungle with the health that she is known for. However, I don't fully understand the clear strategy. I know you set up your human form W at a number of the different camps, then use your cougar form W to jump with the resets and clear the camps super quickly, but I'm not sure what the exact details are. I'm also not sure what the skill order is for levels 2 and 3, however I know you have to start W to get the setup right.
There are probably more that have unique clear paths, but that's all I can think of right now. Full clears will be the most common that you take for your first clear, but it's really up to you which one you do take. Giving camps to your laners is nice, but I usually don't if they don't ask. However, I'll always give it if they ask unless I'm either doing my first full clear or I'm a buff reliant jungler (someone like Amumu or Diana who relies on having blue buff to clear effectively). Jungle is a role that requires a lot of game knowledge, for example, if you see the enemy jungle show on the opposite side of the map, immediately go and take an objective on your side of the map. You won't get there in time to impact that gank, but you can make them lose valuable resources for it. An objective could be ganking one of your lanes if there's an opening, dragon/rift herald, or stealing enemy jungle camps. A gank in a lane where it's an easy gank and you can easily do something afterward is ideal, but you never, ever want to let them gank for free. Take their camps or their lanes, your choice depending on the situation.
For ganking, this is pretty much just don't be an idiot. If your Riven top lane is feeding a Darius, it's highly unlikely that she'll provide enough of anything, even in a 2v1 fight, for you to do anything there. You'll have to kill the Darius basically yourself, and if he gets away, she's likely to overextend and die for it, so make sure you're fed enough to kill him in a 1v1 fight before you go anywhere near to top lane. Sometimes, laners will tell you to leave them alone and do things elsewhere. If a laner tells you this, I don't care if you think you can get something good in their lane or not, listen to them. Enemy jungler is camping your Yorick top lane? Go camp the shit out of bot lane. He's going to get smart and be a giant distraction, or get smart and not push so hard and just stay under turret forever. If he decides to be a giant distraction, he's sacrificing his lane on the knowledge that the enemy jungler is there permanently and you can do something elsewhere on the map without fear of him being there, so do it. Camp the shit out of bot lane in return; he's sacrificing his lane to try to let you win the map for the team, so do it. Whether he's begging for ganks or telling you to go somewhere else, go somewhere else and get other things around the map. Lee Sin camping top? Every time he shows top lane, go bot, kill them, push lane, get dragon. He's 1 player falling behind, while 3 allies get ahead in that situation. 2 enemies get ahead, and 2 enemies fall behind. Pretty much, if a laner is getting camped, they might choose either by stupidity or by intelligence to sacrifice their lane so that you can win the map for the team, so don't just sit there and farm.
Lanes that are pushing towards your turrets and lanes that have hard cc for you are always easier to gank. It also doesn't hurt if you play a jungler with your own cc, so that you aren't reliant on laners to be smart if you want a gank to be successful. They can be as boosted of monkeys as they come, but if you're smart and you can do everything yourself in that gank, it'll go well. However, if you can't do everything yourself, you might find some problems if they don't follow up when you go in. If this happens, disengage immediately. It's not worth anything you can get them to blow. If the enemy laner flashes away from you and you can't get the kill anymore, take the summoner advantage and back off. No gank is worth you getting killed if you don't get something of equal value in return. 1 for 1 trades when you're even or ahead are awful, but when you're behind a 1 for 1 can be pretty worth because the enemy you killed is probably worth more gold than you. What can also be used to determine worth is objectives you get in return. Nunu flash q smites the Cloud Drake from the enemy team, then dies? That's not the most worth trade, because it is just a Cloud Drake, but it's not bad. It's about as worth as a 1 for 1, depending on how fed the Nunu is. He does the same thing for Infernal? It doesn't matter how fed he is or how much shutdown he just gave the enemy team, that was well worth it. Just don't be an idiot and follow him in if you're a laner. Let the yeti rider die and take the HUGE advantage that Infernal Drake gives your team (8% bonus AD and AP per stack! That's HUGE! Especially with a high scaling team).
For diving, imagine the turret is an extra champion. If you would take a 2v2 with that laner, you could probably take a dive with that laner. If you're a big fat tank with decent damage, you can almost always take that dive, especially if your laner is ahead and you take the aggro.
Summary: the jungle is all about game knowledge and being smart. Punish the enemy jungler for showing himself, just don't be an idiot. Things you would expect to be worth may not be, and things you would expect not to be worth may be. Study up on game knowledge and make sure you aren't a mega moron and you can succeed as a jungler.