As usual in such conflicts, reliable information is hard to come by and you have to rely on information that is provided by the parties to the conflict and see how much of it you can verify.
While it may not all be objectively true, it still gives you a good view on how the parties see the conflict developing.
First of all, it helps to keep in mind, that there are three entities in play here: Artsakh (Nagorno-Karabakh Republic), Armenia on the one side and Azerbaijan on the other.
From Artsahk sources, I have the following information about civilian costs of the conflict (Russian original/English translation added by me):
From Armenian official sources, losses of Azerbaijan military forces (doesn’t need translation, numbers are obvious):
From Azerbaijan sources, a map of the current situation on the ground according to them (note that there is a difference between Nagorno-Karabakh as a province/autonomous region of Azerbaijan and Nagorno-Karabakh as a Republic):