1) What is the setting for this/these species? Do they have their own planet? Do they live in a different universe entirely? Do they live on earth? Pre-human, coexisting with humans, at the same time as but not in contact with humans, or post-human?
2) What is the species status on this world? Are they the prominent sentient species? Are they the only intelligent species? Are they populous, or in danger of extinction? Are they the end-all carnivore, an opportunistic omnivore, a gentle herbivore? Warlike or peaceful? Do other species coexist peacefully, or fear them?
3) What other species do they coexist with? Do they have to live with/around humans? Similar species? How has it shaped their culture/habits? Are their prey animals unintelligent? Are the species around them real animals, or other "original species"?
4) How far have they expanded? Somewhat tied into question 2. Are there many, or few? Do they live in an isolated pocket, or do they dominate the entire planet? Just one continent, only the accessible parts, or all of it?
5) Are there different species or variations within the world? Some suited for a harsher climate, some suited to camouflage in the jungle? If they live in different ecosystems, do they have different prey, and different tactics for procuring food?
These questions are obviously more involved with those who have very developed, especially multiple, species. They're also rather helpful in developing your species.