I can’t tell you how you can or should do it, and can maybe jes’ barely describe how I do it. It really is acting, which is ‘acting as if’; you have to understand the song’s situation and the emotion you are to portray, and it helps a great deal if you’ve felt that particular emotion a lot, or at least once, though very intensely. One of the reasons we performers are such flakes is that we tend to feel things very intensely; it’s makes us good at this job, and sometimes very bad at relationships. If you’ve ever wondered why some of the best of us die so young, it’s because a severe case of arrested development, depression or bipolar disorder can actually be considered an asset, in this crazy business.
You don’t necessarily have to have been in the specific situation you’re singing about; a similar emotion will do very nicely, thanks, but you have to get all the physical and rote memory stuff out of the way, before you can really begin to emote. If you’re thinking about remembering the bridge lyric or where to take a breath, you can’t be ‘in the moment’ which is where you need to be, along with your memory of what that emotion feels like in your body, in order for you to do the thing. And the thing itself is really multitasking, which doesn’t come naturally to anybody, no matter how many teens tell you they’re “studying” with headphones on, in front of the TV, while texting and chewing gum, even if they also have a book open. This is because a small part of your brain needs to regulate your endocrine system, so that you don’t over-emote; if you actually break down and cry, your resonant cavity fills up with phlegm, your mascara will run, and if you’re sobbing, it’s hard to get a breath for that next chorus.
The other thing is that you have to be utterly fearless to put your real emotions on display for others to hear in public; you have to open yourself up and be nakedly vulnerable in a way that most mundanes, straights, civilians, muggles (pick your term) will never understand.
So in summation, you have to have the song cold, you must feel the appropriate emotion in your body, (but not too much) and most importantly, allow others to hear and touch the deepest part of your soul. In Broadway terms, this is known as ‘giving it up.’