It's clear that the focus is on humans and Earth, but as the question was framed about the Federation and not just Earth, we should at least consider the tens of billions of non-human civilians too.
Those "bunch of aliens" probably make up the bulk of the Federation's civilian population (even if humans are seemingly more numerous than any one alien species). So in asking the question, one cannot consider an answer without including them.
And in that sense, it's anyone's guess what civilian life is like on, say, Andoria or Coridan or Betazed or Trill. Other than humans and Vulcans (and maybe Denobulans) we have no real sense of the day to day existence of most Federation species, even those fairly similar to humans. Hell, we know a lot more about the civilian lives of Cardassians, Ferengi, Bajorans and Klingons (all non-Federation species).
For bizarrely different lifeforms, like Caitians or Xindi, there's simply no way to guess unless the writers choose to show it.
I'd imagine, as other have stated, that human existence isn't much different, just minus the daily grind associated with paying the bills. Some humans, I'm sure, "do as the Romans do" when they're living on alien worlds (as seen in DS9) and most of the not-crazily-alien aliens living on Earth probably reciprocate (as seen on ENT).
