Think about the motivations of your various characters. What does person A want? Does it differ from person B? Can you use that to create problems in the story?
Opposing ideology/belief systems. "I believe in aliens and you don't."
Different ways of doing things. "I always rinse the dishes before I put them in the dishwasher, why on earth don't you?"
Competition for scarce resources. Imagine siblings fighting over the last chocolate in the box.
Build a great wall of conflict. Be clear about what your main character needs and wants and then build a wall to stop him getting it. Think of each setback and obstacle, both internal and external, as a lump of rock that builds the wall.
Fight your own battles. Conflict will be authentic and compelling if you write about something that touches you passionately. Just avoid preaching!