First of all, you have to develop a very good reputation during your course work in the graduate school which will help you to choose the advisor of your own choice. Then, find the advisor who is teaching or working in the area of your interest as it will help you the most in your research work.
You should choose an advisor who has a good reputation amongst the alumni, in his or her specific field. You can ask your seniors about the competency of the advisor or you can simply search it for yourself. If you will be able to choose the advisor who has good reputation, your thesis will be completed well in time and you will have the best learning experience.
You must consider the availability of the advisor which you want to choose during your graduate school. Make sure that your advisor spends reasonable hours on campus so that you can easily meet with him to discuss your work.
Don’t select an advisor with whom you have some kind of disagreements in the past. Keep in mind that it is extremely important for you to choose an advisor with whom you can have a good interaction because your research work will take time to complete. Simply, search for the advisor for whom you have respect.
Try to choose an advisor who has a success history. You can ask for the advice of your current teachers who are teaching in your school or you can simply ask former students who have done some remarkable research work.