A lot will depend on genre, of course. (One great reason for loving fantasy and sci-fi is the huge scope for creating your own peoples and civilisations).
However, one fundamental here is that there will be a major people/alien being group and minorities around it. Of course there are a lot of stories to be had in showing how the major group treats the minorities and do they rebel against ill treatment etc? But even where there are no direct clashes on the grounds of racism etc, what do your peoples need to survive and how do they get this? Is there a have and have-not society going on?
You will need the suppliers and the supplied-to. You will need the ruled and the rulers. Different peoples will have specific needs so how does your world cater to those needs? What are the belief systems? Do the peoples share common values/faith etc or not?
And, to add spice to the mix, there will always be those characters who defy their society's expectations of/for them.
So have fun creating your peoples!