No you don't have to entertain her, that's the first mistake guys make. But yes you should lead the interaction and do something fun together. If your problem is conversation, then you should find some fun date ideas. You don't have to have some deep spiritual conversation on the first date. This one girl I know, I took her out at night and we playd that game where you knock on peoples door and hide. we barely had 20 minutes of conversation the whole night. The next day, she was the one phoning me to get together again! So the first thing is to find a date that entertains both of you.
Then when it comes to convo, to be interesting, you have to have interrests, but I would also say you have to be INTERESTED.
So many times a girl says a guy was interesting, when the girl did 80% of the talking. Why?
You may think you are listening to them and holding on a good conversation but odds are you really aren't processing what the person is saying. It is so rare that people do this that when you actually do it, it makes a difference and people can tell. 99% of the time we are thinking about what WE are going to say!
One of the biggest things I've learned that has led to my success socially is that people love talking about things they are passionate about or have a view on. After enough practice actively listening you will be able to easily identify topics that you should cherry-pick and will be able to easily thread conversations. From then on, YOU'RE IN!
Here's the simple formula:
You need to pickup on keywords. Girl says "I went to the beach with my dog" Keywords BEACH, DOG. Now you have to think, what more can I find out OR how can I relate to those. YOu can ask her more about those, or you can talk about how they relate to you.
I would also recommend checking this book out to learn more: link