Well you should start it when you are calm of course. I'll get to how you can get there but first you'll have to both be in a situation when you and the other person are willing to talk. If you can see that the other person is busy, don't bring this up because that is not only inconsiderate to them, but it'll get nothing done and having a second difficult conversation is awkward. So when the right time comes, just say "hey, can I talk to you about something?" in a calm, casual voice. If they say yes, start with a non-aggressive statement. Usually apologizing works as a starter for these things so even if you don't think that you should be apologizing, just do it anyway to ease the tension. If they say no, then just say okay and hopefully try to bring it up some other time.
I've recently had to have a difficult conversation with some people and I admit, it was hard to remain calm especially since I am an emotionally sensitive person. I could just feel the tension in the room and it was extremely uncomfortable. Even though the conversation didn't go as planned due to various circumstances, I must say that it helped that I had written all my feelings down beforehand on a sheet of paper and I had that with me. Writing things down helps you review and reflect on how you feel and that will help you think about them logically rather than emotionally. When you write down your feelings, whatever you do, do not make accusations. You need to just focus on how you felt without thinking too much about what the other person did to make you feel this way (that will come secondary). Some people call this method the "I statement" where you start everything with "I felt" or "I believed" or "I thought" and omit words like "you", "he", "she", or "they" as much as possible because they can be seen as accusations.
Since this conversation is a difficult one, attacking the other person for their faults will only make things worse. After conveying how you feel, instead try to acknowledge what you can do better (even though that may not be a lot, there is ALWAYS something you could've done better so don't be cocky and say that you did nothing wrong because that is off putting and will make you come off as arrogant) and then leave it open for them to do the same. And if they choose not to own up to some of the things they've done which is what happened with my recent conversation, then you know that they aren't people who are worth being around since they are either not putting their best effort into the conversation and/or they are just socially incompetent and inconsiderate.
And however this will end, remember that once the glass (which is whatever your relationship was with this person) is broken, it'll never be the same again. You can try piecing it back together but you'll never get rid of the cracks. In other words, don't expect that things will be the same after this conversation. You need to also try making and thinking of a plan of how you will proceed afterwards. Most people are either not mentally prepared or just haven't really thought about what will happen afterwards and thus after the conversation, things are just awkward and nothing gets solved. So that's just another thing to keep in mind.
Okay I hope this helps you out a bit. Good luck!