Consider your genre (and sub-genre). Certain genres have traditional methods of establishing conflict. For example, in a mystery, there must be one or more criminals who commit one or more crimes and a protagonist whose job it is to solve the crime(s). This creates natural conflict between the evildoer and the sleuth. Romantic fiction requires conflict between the two main characters. This can be internal (for example, one partner's inability to commit) or external (feuding families). The conflict keeps readers wondering if the characters will ever get together and their curiosity will keep them reading.
Consider your character. What type of life does she lead? What does she do for a living? Where does she live? What kind of person is she? What are her primary relationships? The answers to these questions can suggest potential areas of conflict. For example, a young widow who lives alone, works from home and does not socialize may experience conflict when her new neighbor tries to befriend her. Or a police officer may catch a case that is not what it seems, leading him into a secret and life-threatening investigation.
Create a purpose for the conflict. Conflict for the sake of conflict will get old quickly. Each conflict should drive the story forward as the protagonist overcomes his obstacles. Show the reader why it is important for the hero to experience the conflict and how it changes him (preferably for the better). Explain what the character gains from overcoming conflict. The resolution of each minor conflict should help the hero overcome the central conflict of the story. For example, a mystery sleuth may have to overcome an attempt on his life, his personal aversion to prying into people's lives and an argument with the wrong suspect before overcoming the central conflict of solving the murder. But each of the minor conflicts should give him new information that helps him solve the case.