How do you bring up a difficult topic?

I am just wondering how would you bring up a difficult subject to talk about. I've realized that when something is hard for me to say, I'll hold back emotions, and I'll talk in a very robotic and monotone way, so that my voice is clear, but then my words will come across as being untruthful, and they will think I'm lying to them. However, if I talk with emotion, I'll have a breakdown and my voice gets muffled, and they can't hear my words at all. So it's either I deliver the message in a robotic way that is not believed, or I break down crying and no words can be heard at all. Both don't really have a good outcome. 

I also don't really know how to start going into a difficult topic, so it starts off sounding sort of too lighthearted, but then the words are more serious than that, so it comes across as sounding weird and nothing matches. My facial features don't correspond to the words I'm saying, so it's just confusing for them to follow what I'm trying to talking about, and it's confusing for me to figure out how to deliver the message in a way without making things seem too dark, gloomy, and serious, that ruins the pleasant mood that they were previously in, and just introduces stress. 

I don't have a specific difficult topic to talk about though. It's just that this is what I generally notice happens when I try to bring up more serious topics that seem to be more personal to me in nature, that are either hard or painful for me to speak about. I'm just wondering how others would go about handling these types of topics and discussions.