Your time as a graduate student will be filled with exciting challenges and experiences. The first is of utmost importance: finding the right graduate supervisor for you. You’ll want someone who shares your research interests, who can help you achieve your academic goals, and with whom you feel comfortable sharing ideas. Effective communication and a good working relationship with your supervisor will have a huge impact on your entire graduate experience. Although achieving your academic and research goals will involve contributions from many people, having a good understanding of the expectations in the student-supervisor relationship from the start will help you identify the right supervisor for you. This guide will take you through the steps for selecting the ideal graduate supervisor: Whether you’re an undergrad applying to a graduate program or a graduate student thinking about a researchbased degree, this resource will help you navigate an important step in applying for grad school.
Talk to the professor first and see how you feel about that person - are they approachable, communicative, professional, etc. Then see if research interests match. Perhaps you should talk to more than one potential advisor before making your final choice. Don't let money (i.e., stipend offered) be the sole motivating factor behind your choice. You can also talk to peers as well as administrative personnel in the department to get their opinions as well.
All what is said here is great. Once you find one based on these advices , ask for one month internship. Asking previous mentees is very important. Preparing a plan of what you are looking for is mandatory. Give score. Magnify what you find (and overrate the negatives).