I incorporate ear training with general study of music. When a student does something inaccurate at the piano I will ask them to do it again after listening to how it should be played. I will not say in words what I am doing, simply play and let them listen. More often than not they will realise what needs to be done, otherwise simply hint them towards the answer. I only do particular ear training excersises which are tested in examinations with students who are sitting examinations (like humming back a phrase, or clapping a rhythm, or singing the lowest, highest or middle note of a chord etc), otherwise I will never simply pull ear training aside alone and study that.
I find it is a big challenge to get a student to listen to themselves as they play. Some can get it, some simply cannot. For those that cannot I will record them and play back their playing so they can forget for a moment about pressing notes down and listen to the result of their work. Often many of them cringe at listening to their own playing. I will also record myself and then ask them to determine which recording is mine and which is theirs and why can they tell the difference. I always encourage students to record themselves when they practice at the piano. Unfortunately not all of them have access to recording tools.
I find also the more a student actually listens to piano music the more accurate they can actually listen to themselves. You might be surprised how many students who study piano NEVER actually listen to piano music!! I always encourage listening to piano music and reading sheets at the same time, this is essential training imo.