NPCS:
Norah Kalesy (Varanas Gates - 49.7, 80.0)
Myden Neil (Varanas Gates - 34.0, 21.2)
If there are others, I don't yet know of them.
Event Timer:
I'm led to believe this "event," as Norah calls it, is set to run on a timer of sorts. Since it's all about constellation pets, and it's currently the month of June (Gemini month), the current pet on display is a Gemini pet. So the pets may change monthly, which means you only have 30-31 days to get the pet you want. However, there are 3 pets for each elemental affinity (water, wind, earth, and fire) so you'd have a total of 3 months to collect elements for the pet you want. The months will obviously not be consecutive.
I could be completely wrong about this, but it seems logical. I just don't know if Runewaker would actually plan something that dynamic.
Pet Previews:
Conveniently, Norah has a pet on display at her side! Right now it's a Gemini pet. That means when you do the event you're going to get WIND elements (I assume) because Gemini is a WIND sign. I assume the pet will change when the event shifts to feature another zodiac sign, which means the element rewards in the event will also shift appropriately. For example: next month is July, which is the month of Cancer, which is a WATER sign. That means the event rewards will probably be WATER elements.
Again, I could be completely wrong about that. Either way, it's nice to see what the pets will look like before we invest in acquiring one.
Machines:
As Nasira said, run to the opposite end of Varanas bridge and click on one of the machines. When the dialogue box comes up, read the manual so you know how to play the "game." Then start the machine. Basically you get 3 color "spells" and you have to use the appropriate color associated with the colored orbs on the machine. There's 5 orbs on the machine, so you do have to be fast, but I'm sure there's a way to time it appropriately. For orbs you miss (they explode), you lose points. For orbs you match successfully (they disappear), you gain points. For simply using the device you will get elements. For example, I played it once and got Wind Element x4. Needless to say, I performed poorly. xD You can only play once per day.
My best guess is that if you can play the "game" well, you will receive Universal Components. You can exchange those at the near-by NPC...maybe for more elements? It probably speeds up the pet process. So I guess we all better practice matching colors and good luck to the color blind! o_x
Transmuter:
Ok so now what do you do with the elements you get, you may ask... Well it's transmuter time now! ;D They combine in stacks of three, so I split my stack of Wind Element x4 into Wind Element x3 (extra one stays in my bag). The stack of 3 I put into the transmuter and merge it into Wind Stardust x1. There are ultimately 5 levels (or tiers, you could say) of each element, but not all of them are necessary yet. The 5 levels are as follows: Element, Stardust, Star Sand, Star Stone, Star Diamond. If you think this sounds a lot like tiering, you'd be right; it's exactly like tiering. Standard charge rates apply. ^-^
Newborn Constellation Pets:
As you all know there's 12 zodiac signs, and thus 12 possible pets. The zodiac signs are grouped by 3's into 4 element categories. Aquarius, Gemini, and Libra are WIND elements. Pisces, Cancer, and Scorpio are WATER elements. Capricorn, Taurus, and Virgo are EARTH elements. Aries, Leo, and Sagittarius are FIRE elements.
The first step is to aquire a pet in its newborn stage. You will need 1 Pet Crystal. I have no idea where this is from yet. I guess we'll find out in time.
The second thing you will need is Star Sand x3 with the element attribute as the pet you want. If you want the Gemini pet (a wind element zodiac pet), you will need WIND Star Sand x3. As mentioned previously, Star Sand is the 3rd level of an element (27 Elements = 9 Stardusts = 3 Star Sands).
Adult Constellation Pets:
In order to get an adult constellation pet, you must first have a newborn constellation pet (see above). You will also need 3 Star Stones with the same element attribute as your pet. If you have a Gemini newborn pet, you will need WIND Star Stone x3. As mentioned previously, Star Stones are the 4th level of an element (81 Elements = 27 Stardusts = 9 Star Sands = 3 Star Stones).
Teh Beyond! O.o (Speculation Section):
The NPC Norah Kalesy seems to hint that there is more to these pets than just the newborn and adult stages. However she says it's up to "you" to explore the rest. And hey...what about Star Diamonds?
To me, I think this is obvious. There is likely a 3rd stage of pet development and if the pattern holds true, you will need your adult constellation pet and Star Diamonds x3. So for example, if you have an adult Gemini constellation pet, you will need 3 WIND Star Diamonds, which are the 5th level of an element (243 Elements = 81 Stardusts = 27 Star Sands = 9 Star Stones = 3 Star Diamonds). Tiering is a pain. -_-;
That's all I've puzzled out so far and I hope that it helps!

I'm not the best at explaining things and I'm long-winded, so if anything was unclear please let me know. Feel free to add your thoughts and speculations or if you have additional information, post it! I'm really intrigued by the event and hope we can find out more. :]