After reading your question and the very good suggestions offered by the first answer above, another possibility occurred to me which you might want to consider. Why not take the time to write out your message to your parents in the form of a letter? You could do it in complete privacy, say everything you want to say, and write several drafts of the letter, if necessary, until you are completely satisfied with it. That way you wouldn't have to deal with potential questions, emotional reactions, or other interruptions while you were still in the process of trying to explain. While you were writing your letter you would almost certainly think of more details than in a personal interview. The personal interview would still have to come, of course, but it might be more comfortable for all three of you after both of your parents had had an opportunity to read the letter and to discuss it between themselves. This is just a suggestion for you to consider. Good luck!
There is no way an eNotes editor or participant can tell you "the best way" to have the discussion(s) you are anticipating because we don't know you, your parents, the type of relationship you have, or the additional issues that may figure into the explanation.
There are a several studies showing that homosexual people rarely get negative reactions from friends and family, they seem to take it much better than expected.
You need to do lots of preparation before opening this discussion. Make sure you have information immediately available to be able to address, answer, reassure, redirect - whatever you anticipate might be needed for whatever reactions you can see possibly arising during the talk. You might find someone other than your parents and have the discussion with them first for "practice" in presenting your reality and the information you have found to support your presentation. This person could also serve as moral support for you as your parents process the conversation.
As in all cases when communicating hard topics to people you (hopefully) love and respect, try to remember to stay calm, loving, respectful, and patient. Give them honest answers and lots of time. Expect more than one discussion. Good luck!
If you love your parents, do not tell them ... This is my opinion!!!