So let's say you feel close to someone, there are many ways to bring this up. For example: "I had the most interesting session yesterday with my counsellor. He/she helped me understand that I could examine my emotions and question them rather than give them rein." Another way to bring this up is to point to your progress (with a close friend). "I just noticed that a year ago, this remark (comment, feedback, interaction, whatever) would have flattened me. My counsellor helped me and I'm better able to handle it now and see my choices in responding." Does this sound useful to you?How is your opinion of someone altered if they tell you they are seeing a therapist?
I am generally glad to hear it -- whoever they are. Who do I tell?
I'm just guessing, but I suspect you are asking this question because you might want to tell someone. It's absolutely no one's business, but if you begin to feel close to a friend or romantic interest, then it's healthy to not have secrets, to be open about your past and about the future that you are working towards. Keep in mind that much of depression is chemistry and none of depression is your fault.