The new jungle has a couple of changes since the last major jungle patch:
1. Camps now scale with the average level of the players. You receive exponentially more gold and exp if you kill a camp that is significantly higher level than you are. That means, if you are behind in levels, you can catch up faster.
2. There is a new Wight camp near the blue buff on both sides. It is a single-target monster and gives equivalent EXP and gold as if clearing any other full camp. It's mostly there to give the blue side top and purple side bottom lanes something to kill if they push back their lanes far.
3. The "new meta" is to get a leash from the bottom lane pretty much every time, not to always start blue. This allows for a more efficient leash.
4. All full-build jungle items (Wriggles and the Spirit items) will give bonus gold for clearing camps. Wriggle's Lantern gives a flat +20% increase to gold from the jungle. The Spirit items will gain a stack of gold every 2 seconds, maxing out at 80 stacks. Killing a large creep (e.g., the large creep at a camp, any buff, or dragon) will cash out up to 40 stacks, gaining 1 gold per stack. However, the removal of lifesteal and the flat attack damage makes Wriggles completely useless. Finishing your Spirit item usually means you'll gain 500ish gold per 10 minutes as bonus.
5. Spirit Stone and all subsequent Spirit items return 8% of damage back as health and 4% of damage back as mana. This sustain is phenomenally strong, especially the mana regen.
6. Dragon now scales with the game. You gain more gold the later the game, so it's no longer useless to kill him after 25 minutes. If you get the chance to kill him safely, always take it. A 25-minute dragon is almost 300 gold per person, which is +1500 global gold.
The strategy of these changes involves more gold and better clears. Riot wants the jungler to basically have the same gold income as a normal laner. Gaining Conservation stacks on a Spirit item means you also don't have to only farm the jungle. You can take up to 3 minutes without farming a camp and still get the benefits of the extra gold income. This means you can (and should) provide lane support and ganks.
Junglers are more fearsome in teamfights than they were before, so full-tank junglers (who don't rely on snowballing) are the current group of strongest junglers. Kha'Zix and Evelynn are also really strong because the current jungle also doesn't require you to farm as much as it did before. You can get away with constantly ganking, and only clearing a camp just to reset your Conservation stacks. Falling behind in levels is almost impossible.
As for trinkets, there are two trinkets to get: Warding Totem and Sweeping Lens. The warding totem is picked up by all 4 people in lanes usually, and the jungler usually takes sweeping. The warding totems give a 60-second ward every 180 seconds. At level 9 these upgrade to 120-second wards every 120 seconds. The Sweeping lens will reveal stealthed wards in a small radius (about the size of an Amumu ultimate) long enough for you to kill them. The laners usually take warding trinkets so they can stay safe, and the jungler usually takes a sweeping so he can make sure objectives stay warded only by his team.
Lastly, these trinket changes made changes to wards in general. Green wards weren't changed, but each player can only place up to 3 at once. Adding a fourth ward will remove the first one placed. Pink wards were given 5 health (instead of 3), and they are no longer invisible. Instead, pinks are visible if you are in range of sight of them, but they also last forever. Pinks are really good for warding places not normally pathed directly upon, such as:
• the bush between mid and dragon grants vision of the river
• the bush between mid and baron grants vision of the river
• the "ramp bush" entering both sides of mid lane grants vision of the river and an approaching mid-lane gank from behind
• the "tri bush" on top and bottom lane is the best place for a support to put it because he can control the bush for ganks
• the bush behind red camp is also pretty good for a support to ward because granting a small vision range over the middle of the river and also vision of anyone trying to gank from behind dragon or baron. If your tribush pink is constantly getting killed, placing one in this bush accomplishes almost the same thing. The person can't get behind dragon (and into tribush) without stepping past this ward.
It's good to place pinks in a bush so that the potential for one to get spotted is much smaller.