What sort of questions should you ask professors to establish a relationship?

First of all, I think you should definitely take a direct interest in the contact that your professor is teaching you. I would ask critical questions (How's? Why's?). This will let you professor know that not on are you actively listening to the content, but you genuinely care about the content and seek to better understand it as well.

If you are also interested in the subject matter, don't be afraid to ask more personal questions to your professor as to what made the interested in their specific career field/content. Why are they passionate about their fields? What were the steps they took to becoming a professor? Who or what inspired them? In my experience, professors are always open and even excited to share their journey's with their students, so don't be afraid to ask!

When you want to establish a good relationship with a teacher you should be willing to pay interest in the subject that the teacher is dealing with. Not only paying interest but also being proactive about the topics that he is going to take up in his class.

When you like a subject the doubts arise in your mind about the different topics that you have learnt. Br yourself and open up to your teach about what you feel and what is it that you are stuck with.

Getting a teacher to like you may open an opportunity for your teacher to help you better grades. Perhaps you just want your teacher to cut you some slack? Maybe you want to be a bright spot in their day, without the stigma of being the teachers pet. You might also want them to like you so that you'll be noticed. 

More than asking questions about the subject you might want to be good as a student. Teachers appreciate well behaved students and tend to have a corner side for them even if they mess up. Teachers will give you a second chance and would love to get to know you and help you improve. Most of the times you dont have to try to get the teacher to like you. It just happens. :)

A good start is to get to know yourself better and develop a familiarity of how your personality traits fit with various career areas and then do networking to get to know your career area of interest through various networking means concentrating on interpersonal communication which allows for two way dialogue.

Getting to know yourself and how your personality traits relate to people involved in various career opportunities is very important in your decision making process. During my many years in Human Resources and College Recruiting, I ran across too many students who had skipped this very important step and ended up in a job situation which for which they were not well suited. Selecting a career area is like buying a pair of shoes. First you have to be properly fitted for the correct size, and then you need to try on and walk in the various shoe options to determine which is fits the best and is most comfortable for you to wear. Following are some important steps which I developed during my career which have been helpful to many .