There are basically three aspects to gameplay in your typical RPG: Plot, battles, and puzzles. Most RPG's (like the Final Fantasy series, for example) have you spending most of your time on battles, a good chunk on plot, and a rather small amount of time solving rather trivial puzzles. Fate of Io puts less weight on battles, a bit more on plot, and a lot more on puzzles.
If you are a devout Final Fantasy fan, the word "puzzle" probably makes you cringe. Your first thought is probably the sphere puzzles in Final Fantasy X, which basically involved swapping various spheres in and out of various holes until they matched what the designers were looking for, with almost no hints to work with. Try to remove these thoughts from your mind (if, indeed, you haven't already suppressed the horrible memories). Fate of Io puzzles will be more akin to those found in The Lost Vikings (an excellent SNES game which I recommend to everyone).
Each character in Fate of Io will have unique abilities. For example, Dell can fly, Rheya is good with technology, and Enna can shoot from a distance. In order to solve puzzles, the characters will have to combine their abilities.
Most puzzles will have multiple solutions. The easiest solution to each puzzle would typically be a "brute force" method that isn't hard to figure out, but also doesn't give good results (it might leave your characters with low health, etc.). On the other hand, more complex solutions might take less work and leave the characters ready to move on quickly. (Open question: Should we award players for using clever solutions? Perhaps keep a tally of "style points"?)
This essay on puzzle design should help you get an idea of how to design good puzzles.
(This will not necessarily be in the game.)
Syne, Dell, Enna, and Cade need to find their way into one of the Pylos mining facilities. The door is guarded by a couple of big, tough-looking men wielding spears. The building is in the mountains, and there are a few sheer cliffs around. To get past them, the player could:
Just fight. With four against two, and tough fighters like Syne and Cade, the player would probably win, although the guards are probably somewhat better fighters. Also, they might alert others, which would make the rest of the raid much harder.
Lure the guards away into an ambush. With the cliffs about, there should be plenty of opportunities for the characters to push rocks down on the guards. Additionally, Enna could stand up on a ledge, out of reach, and shoot down at them. Dell would be the ideal one to lure them, since he could fly out of harm's way when the guards got close.
The people of Titan continent don't know about Antareans (despite Kydran being one), and probably have not prepared for intelligent flying creatures. Dell could probably fly around the building and find an open window or some other high-up opening. Once inside, he could either find a way to let the characters in, or to temporarily draw the guards away from the front door. In any case, this is an excellent solution since it requires no battle at all, and is not likely to alert anyone to the characters' presence.
Syne and Cade are Pylos workers. Assuming they still have their uniforms, they might be able to walk right up and talk to the guards. Maybe if they try to just walk right in, the guards will stop them and ask for ID, but if they chat for a bit first, they could gain the guards' trust and get by without it, or they could trick the guards into leaving their posts.