Temples have an entrance on one of the short sides, a ‘Good Side’ lengthways with both chests (as shown by the Lime Glass to the right) and a ‘Bad Side’ with no chests (Red Glass). This can be mirrored, so often you wouldn't know which side (left or right) the good side is without going down the stairs.
If the Bad/Good sides are split North-South, the Good side will always be on the South side. If they are split East-West, the Good side will always be on the East.
Alternatively, you can also tell apart the sides using chunk borders if you are close, if you prefer doing it that way.
It seems confusing but can be very easy to work out with a simple F3 check. If you are approaching the side of the temple, and facing North for example, you know you are on the good side.
In Draftout, with the addition of Bird's Eye View, you'll often see the Temple in the drafting phase, but you might not necessarily instantly be able to tell which side the entrance is on (credit to Feinberg for the screenshot, right).
One helpful difference between the mostly symmetrical structure is this overhang of 2 blocks above the entrance (circled, left).
It can sometimes be hard to make out, but in the above screenshot, if the entrance were on the right, we should be able to see these two blocks on the right from Fein’s perspective. So the entrance must be on the left, hidden by trees.
(The 4 stairs at the bottom of the entrance can also be an indicator if you can see them.)
If front and back are obscured by vegetation, and you want to know which direction to go, you can use F5 to see inside. If you see this raised line of blocks inside (in the screenshot it’s that half cobblestone block peeking out), then you are closer to the entrance. If you don’t see it, then you are nearer the back (i.e. the top of the stairs).
The routes discussed below are set out in this video, but more explanation is given on this page if the demonstration is not enough, as well as information about the goal itself (for example, the likelihood that a given goal will be achiveable from a Jungle Temple).
No Items
(OUTDATED -- SEE VIDEO ABOVE)
Okay yes, it is just solving the puzzle.
As or before you are entering the Temple, you can check your direction. Here, we are facing South, meaning the Good Side, and hence the Puzzle, will be on our left (East).
You:
Flick the far lever down.
Flick the close lever twice.
Break the far lever and take that one with you.
If you are willing to take some timeloss post-goal, you can just flick the far lever instead, solving the puzzle as normal.
The puzzle is solved, and you can break the repeater instantly.
To leave, you just place the lever on this block (see below), flick it and hold spacebar at the same time.
If you opted for pace and didn’t punch the lever, you can check the chest for 2 bamboo to craft a redstone torch to place there instead (credit to sujuxi for this), else you have to punch 2 sticky pistons to pillar out.
Pickaxe Back Entry
If you are on the good side near the back, you can dig down straight onto the repeater. In the screenshot, we are side-on facing West, so we are on the Good Side.
Digging on the block shown with light blue concrete (3 in from the back) will drop you right on top of the repeater. You can continue to hold left click to instantly break it as you fall. Technically you can do this by punching the block, but it’s slow so I would only recommend this if the entrance is quite buried.
Bad Side
Breaking these blocks next to the entrance (replaced with light blue concrete) will, if you mine it on the bad side, put you right on top of a dispenser. Once you mine the dispenser, you can mine one of the blocks next to you to put you in the Trap Room. Alternatively, you can just pillar out if needed.
Good Side
This route puts you in a better place to loot the rest of the Temple. On the Good Side, mine the block just 1 block out from the corner (again, marked by concrete). If you face slightly to the front when mining, you will fall through and can immediately start mining the side of this dispenser.
You can then loot the Trap room, and if you need to check the other chest, you can turn around and mine 3 blocks to reach the Puzzle chest.
85.17% of Jungle Temples have 3+ bones for Obtain Bone Block. With a 61.5% chance for 4-6 bones per chest, if you find any at all, you'll have enough.
Pickaxe
If you are making just a pickaxe, don’t craft it until you get to the Temple, otherwise you waste timing breaking the crafting table (assuming you are entering via the entrance). Find the Good Side and craft your pickaxe.
Crouch and mine the corner block – you will be right on top of the Trap chest. If you sneak and select an empty slot, you can right click to loot for bones without falling down (remember to let go of movement keys before you right click otherwise you can slip). If you getbones, of course you can instantly craft the Bone Block with the crafting table next to you.
If not, you can check the other chest. Go next to the stairs and 1 in from the back corner. Again, shift and right click with an empty fist to loot.
These are the blocks to mine (final image). There’s a short from 2 years ago that mentions this way of looting, so shoutout to Camman18.
72.25% of Jungle Temples will have enough Gold for Obtain Clock. Unlike Bone Block, it's possible to only get 2-3 Gold in one chest and more in the other (an example of this is in Variation 2 in the YouTube video). The average amount of Gold in Jungle Temples is 6.06.
Pickaxe
Similar to Obtain Bone Block, we are starting with an uncrafted pickaxe. Place your crafting table on this block. Then we go to the Puzzle chest and check for Gold (the same way as in Obtain Bone Block). If you have enough, you can drop down and mine the dust at your feet. You can jump up and right click the crafting table to craft the clock (and pillar out using the spare plank and the cobble you mined to loot the puzzle chest).
If there wasn’t enough Gold, run to the other side of the crafting table and mine the block next to it, falling down into the hole. You can loot the chest, get this redstone dust next to your feet, and the crafting table is right above you to craft the clock. If both chests whiffed, you can loot the rest of the Temple from here and then leave.
Crafting Table Only
With just a crafting table, it’s kind of a 50/50 whether you decide to loot the Puzzle chest first (see Obtain Repeater – No Items) or just run to the bad side and loot the Trap chest first. If you whiff on one, there’s no easier way to check the other (punching cobble is just too slow). Doing the Puzzle first means that you have less distance to run back, but choosing Trap chest first lets you open your first chest earlier.
This also applies to Obtain Bone Block, except for that goal you could use the Feinberg lever-clip method to loot the Puzzle chest.
Other Goals
There are of course plenty of other goals you can get from Jungle Temples, and more that Temples can contribute to.
With Obtain Piston, punching 3 logs is enough – just remember to only craft 1 set of sticks. Then it’s similar to Clock except you need Iron instead of Gold and you also need 4 cobble.
With Tune a Note Block, it's best to punch 3 logs and run down the bad side to pick up a redstone dust as soon as possible.
With Powered Rail, you can't book craft since the recipe only unlocks if you have a rail, so you will need to craft it normally (6 gold, 1 stick which you could get from bamboo, and 1 redstone dust).
Scaffolding, Crossbows, Use Smithing Table … the list goes on. Knock yourself out.