For me, the people I have told so far have known that I have had a bad depression problem for as long as they have known me. I didn't go up to them and say, "Hey guess what, I am trans, deal with it."
I respectively went up to them and told them, "I finally found a therapist that I have a connection with, this is the first time I have truly been happy since I can remember." And they ALL responded, "That is great! I am happy that you are finally happy and not depressed."
I softened the blow also by asking them questions about some t.v. program. Ask them questions like, "Those documentaries on channel "blahblah" are really good. I found myself watching one on "thingy-majigs" and couldn't stop watching it. One day I turned on the television and saw a documentary on trans gendered people. Have you seen it?" Then the conversation blossoms from there. I didn't force anything. Knowing that they think about trans people before you tell them can have a really big effect on how they respond.
I told one of my best friends not a week ago, and after I told her she put her hand on my knee and when I looked at her she was crying. We made eye contact and she gave me a huge hug and told me that she would love me no matter what. We (me, her and her fiance) are now looking for a place together, and it makes me feel great that I will be transitioning in a house with people who really accept me for who I am.
I am a lucky one to not have found a person who did not accept me. I am fortunate enough that all of my friends knew that I have depression problems, and this is really helping me.