Imagine a blind date. The guy thinks it goes wonderfully -- amazing chemistry; they have so much in common. The girl thinks it's a disaster, that he's a real creep.
Write about the date in the first person, from the girl's point of view. E.g., "I met him at the restaurant at seven. He looked..." (For tips on writing in the first person, click here).
Then, write about the same date in the first person, from the guy's point of view.
If you want, you could also rewrite the same scene in the third person, switching back and forth between points of view. Use some kind of indicator so that readers know where the point of view is at all time. Maybe give the man a few paragraphs, then the woman, and use a line break each time you change to separate the story into sections. Don't switch back and forth too fast, or you might leave your reader dizzy and disoriented.