well, we can start from some basic assumptions:
The 'planet' is likely to be tidally locked. So one side will always face the gas giant, the other will face away. This will dictate the 'day night' cycle as it's based on the moon's orbit, not rotation.
The tidal forces will likely severely flatten any geological features. So you'll have lots of rivers and lakes, but no real ocean. Unless there's enough water to make the whole flat thing one big shallow sea.
You'll have some pretty nasty weather, as portions of the planet would be under the punishing glare of the 'sun' for day's or weeks at a time, before it rotating out of view by going around it's orbit. Unless you've got a dim star (or very distant star), and say, a large hot brown dwarf...then you'd get lots of light all the time from the dim star, and from the brown dwarf radiating as it cools.
For the planet facing side, even during the night phase, the gas giant will reflect a lot of the sunlight, not really keeping it warm (the IR is trapped by the gas giant, but optical is bounced), but also strongly illuminating the surface. Imagine a Full moon....x100! They wouldn't really appreciate a true dark night except for when the gas giant eclipses the sun once an orbit (for hours/days depending on moons' orbit).
The outward side wouldn't have that problem though...so you could have plants vary more by which hemisphere they exist on, than how close to the equator (or poles) they live on, though that would likely matter too.
The radiation band (like earths van allen belts) don't have to enclose the planet, but could sterilize other moons. The gas giants magnetosphere could mean high radiation levels though, possibly suggesting more life is aquatic or subterranian (to shelter it from what radiation there is). Or with thick, radiation resistent hides/metabolisms.
You'd probably have some spectacular, nearly constant (and likely very bright) aurora -- planet wide.
Odd little local custom touch: with the tidally locked planet, and prominent gas giant, they could very well define the gas giant to be their 'north pole', instead of having it along the axis of rotation/revolution like earth. I.e. earth's north pole is tilted 23 degrees to our orbit, theirs would be ~90.