If you interpret something or make sense of it, you construe its meaning. If the new girl in your class asks to sit with you at lunch, you could construe that she wants to be friends. You can never have too many friends!
To make an assumption based on evidence is to construe. You could construe that eating an entire box of cookies might make you feel a bit sick. And you might not want to eat them again for a very long time. The opposite of construe is misconstrue, which means to falsely or wrongly interpret. If you get a poor grade on an essay, you shouldn't construe that your teacher dislikes you. If you do, you misconstrue your work for his feelings.