There are people who never lack conversation topics. If you are not one of them, don't worry. Having an interesting conversation is an art that you can learn.
To go beyond conversations about the weather, education, profession or work, it is enough to raise an unusual topic or bite it from the unusual side. Then the conversation has a chance to turn into something intriguing and unconventional. Point for you!
Sometimes all you have to do is find the anchor point and it will go downhill. How to do it? Listen carefully to the other person and refer to what she just said. If she mentions where she works, ask how she got her first job or what kind of work she wouldn't want to do. If you're ordering coffee, ask where she drank the best in her life. If you are sitting on the couch, talk about your tastes and preferences in interior design.
Let your date get to know you! Talk about what you think, not just what you know for sure and what has been scientifically confirmed. Others are interested in your views and opinions on various matters. Wikipedia should be correct - you don't have to.
If you still don't know how to talk to a newly met person, take a look at the list below and get inspired.