I was deeply disappointed with how
DS9 approached religion, because to this day I've zero idea how Bajorans viewed the universe. Do they believe in Fate or Free Will? What are their notions of Death? How do they explain suffering? One needn't explore this in depth, but a few strong hints can work. In
BSG we heard a great about
eternal return, that history repeats itself in cycles over and over again. Interestingly, the same notion popped up in
Lexx. In
Babylon 5 we knew the Minbari were deeply religious, lacing every day activities with ritual and meaning. It came as no real surprise they believed the universe itself to be conscious, and striving to understand itself via the individual lives of the beings within it.
The only religious idea IMHO explored in detail with a culture in TREK would be the Klingons--especially their attitude towards Death. In this they resembled ancient Samurai or maybe Vikings, welcoming death as what gives meaning to life, with evidently a potentially Valhalla-esque "heaven" awaiting those who die well.
Either way, one explores a culture's religion in fiction by focusing on actions motivated by a given world view. Klingons rush into battle, eager to prove their worthiness and risk death. Minbari, believing themselves part of a sentient universe, seek to meditate and thus understand more. Folks in the Twelve Colonies look for clues indicating where they may be in the Cycle of Time, to know how to go forward. And so on.