I agree with Kamal: basic foundation knowledge in his field, critical thinking, communication skills, dedication, ambission, and hard working are basic requirements. I would add, however, love for what you do and natural talent.
Yes of course, Directing love and natural talent with good methodology, is what I'm talking about. love is not enough and natural talent needs refinement.
Basic knowledge in his/her core field of research, critical and reflective thinking, analytical skills, writing and communication skills, learning attitude, cooperative, capacity to understand others' researches, and hard working are important.
A good researcher student is first of all ought to be honest with self & with others.Then come other attributes such as good brain, readiness for hard work, diligence, cooperation, precision science-wise & language-wise, self-confidence not amounting to arrogance, and respect for those supervising the research.
Good point from Dr. Brenda Jacono. However, readiness for hard work (no. 3 quality in my above contribution) includes readiness for learning & not just for experimental work. The supervisor can use the method of my supervising professors (every nearly 3 months, I was asked to give a concise written report which was evaluated & commented on). This way the student is judged ( Is there improvement or stagnation or deterioration?).
I may add another feature, that is needed by the student (and not from the student) to become a good researcher, which is: a reasonable research project when suggested by a supervisor that can be done in the university in adequate time. I remembered now the story of a friend of mine who went to a Middle East university to get M.Sc. in organic chemistry by research. He was given a project that needed unavailable materials & equipment & he was told to wait, at least, 3 months for their arrival. So he switched immediately into his second favorite subject (analytic chemistry) & obtained M.Sc. and then PhD. I mean we cannot only blame the student. Sometimes or often , those responsible in the university are to blame when there is no good research.
According to my long experience (over 40 years) the best students are curious, hard working, asking good questions, are not discouraged by failures, they repeat their experiments with appropriate controls. Good students are open to critics, they like to share knowledge with other students (in the lab or different labs in the department), they like to cooperate and they are respectful to the staff.