Overall, patience and conversationalism. High quality microphone and internet, and lots of question-asking are great too. My lessons often start with my teacher asking "how was your week/weekend", but I unfortunately give very simple answers to this question because I don't know how to say anything else. So, when my teacher guides me in answering with more than just "It was good," that's incredibly helpful. Also: I am learning French at the intermediate level and I would prefer my tutor to exclusively use French. Even when I ask a question in English (in which case, I would then like my tutor to help me re-ask in French). And if I ask what a word or sentence means, I generally prefer definitions and explanations in French. Never translations unless I explicitly ask for one.

It's not the most important thing, but a reliable and good-quality Internet connection is absolutely essential.