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You need to fit 7 orbs into 7 rings. The ring on the golem's shoulder must be last, or it will try to activate and lack sufficient power. The orbs must all be the same color (black or white), or the golem's power will be divided, and it won't work.

Mixed: golem leaves
All sol: Nyx are killed
All nyx: Sol are killed

From Bill above there's a fourth where it doesn't power up, but is there any way to actually make anything better?

Actually they say that mixing white and black orbs will make the golem weaker. There are 7 black orbs. I suppose there are 7 light too. What if we have to combine all orbs? Because if there is light, darkness is gone. If there is darkness, the light is gone. There is a giant statue holding the sun and the moon.

You put first the white orbs, and then the black or the opposite.

So far, I've:
1)activated the golem without enough power (6 white orbs, instead of 7), and it left.
2)With 7 white orbs, the dark side gets obliterated.
3)I tried placing 4 white orbs, then 3 black orbs, as xxerox suggested, but it left, due to mixed power sources. Not sure how to place white & black to get a combined 'good' result....
4)I haven't managed to place a full set of 7 black orbs yet; its a bit tricky to know what shrines to make a run for. Though watering the trees definitely helps create some spots of shade along that route.

Perhaps its possible to place 4 of one colour, then 4 of the other - so eight in total? there are enough orbs, but again, I'm not sure which shrines to run for with black orbs (after that, the white ones are easy).

No. BUT - what if you place 3 of one colour, three of the other colour, and the WATER orb? (heads off to try it)

place 4 of each colour, because there are only 7 shrines.
I can however confirm that four black orbs then three white orbs gives the same result as four white then three black.

As much as I want it to work, I can't seem to get the water-orb to fit in a shrine-circle. Darn-it.
Now I have no idea...

If you drop a black orb, it will turn white(due to my 1 try there), so it takes quite a bit of planning to get all black.
The seventh orb is the one which fits in the golem's shoulder.
There are four edges. If you hit an edge, it will blow sand particle effects across the screen.
At the bottom right corner, there is a pictograph ruin, clearing up a little bit what you should do for the 'good' ending. Hinted at
..with the balance statue,
...with the archetypal balance of light and dark,
...with the tree-keeper saying that the trees do well in the desert, but with the water needing darkness.
The pictograph displays the golem in the center bottom, two maybe-humanoid figures to the left and right bottom(possibly wearing a ponytail for Sol and a broad, flat, hat for Nxy).
Above followers of Sol and Nyx are pixels of white and black, surrounded by the accompanying indicators. In the center is a pixel of green, surrounded similarly.
From this, we can gather that we need three white, three black, and the water/life orb.
The life orb is the balance between light and dark, useless if only kept in the dark, dead if in the sun too long.
There are at least nine orbs, exactly seven of them starting out black. (There may be 3,4, or 5 which start white, I lost count).
Both the water orb and the Nyx blossom regenerate when they die.
As of yet, I have not found a way to turn Sol orbs Nyx again. I've even tried leaving them at the Nyx dwelling. By the way, this would tend to indicate that Nyx is actually purer than Sol, as it is far easier to ruin something than it is to purify it, generally. But this is unnecessary, as each Nyx orb can go into a separate altar on the same play-through.

And actually, there are four endings plus the balance end. The leaving end is split into either mixed power or not enough power. Then you have all Sol dies and all Nyx dies, then the elusive 'good ending.'

The person with the flower says to take it to the person who likes plants.

the receptacles on the golem fill up from left to right, top to bottom, in the order that you place orbs, regardless of which shrine you use. If you want all white on the left and all black on the right, place a white orb in a shrine first and then alternate.

The only other thing you need to know is that the golem's shoulder shrine will activate the golem regardless of what you've done with the other shrines. As such, if you want an orb in the middle, it has to be last, and it has to be in the golem's shoulder.

Zillix stated on the game's Ludum Dare page that there are only three endings. I think he intended to make a good ending but ran out of time. I don't think there's a life orb.

You need to alternate, first setting a white orb, then a black one, then white, etc. until there are three white orbs on the left of the golem and three black on the right - just as the picture in the lower-right corner indicates (white on the left, black on the right). Then, you have to take the white orb from the golem and take it all the way to... well, I'm not sure about this, but I'm guessing it would be somewhere in the forest. This ought to make the orb green, so that you can have the green orb in the middle (again, like the picture). This would make a very satisfying balanced ending, but I just can't find a way to make a green orb and wouldn't be surprised if it wasn't written into the game.

the 'pictograph', in the bottom-right corner

1. The orb on the golem's shoulder is white, but when brought into the sun, it has a vertical orange timer, like the nyx orbs. Other sol orbs fade to orange.

2. The pixels on the golem light up in the same order regardless of which shrine order you use. Left to right, top to bottom.