Excellent thread, some kids and adults take to the stage spontaneously, some cannot even utter a few words in the beginning. It is the fear of the unknown like a bathroom singer being asked to perform before an audience, here when we are alone or with family whom we know, we don't mind, we express ourselves very well. We have an assurance that either family members won't say anything bad or even if they say something, it's Ok. This changes when we face a new audience, in fact, this is one of the reasons that many candidates with all the knowledge cannot perform well in a viva exams.
I remember during post graduation days, having a podium presentation and standing on the stage taking questions was mandatory. It would be very scary to face strangers and seniors asking questions.We had good teachers who encouraged us to first prepare the subject well,keep it simple, speak slowly and clearly to begin with, do not rush through the presentation. When standing on the stage, instead on focus on one or two whom we know, focus on the general audience without holding sustained eye contact helps a lot. Practicing in front of the mirror and infront of colleagues helps too. After a couple of presentations,it becomes easy, it like a few stammering words and in a couple of minutes we hit the rhythm and start performing.
Trying to focus on too much of matter should be avoided initially, developing a skill to speak from cue words is a useful trick as we can make up the sentences as soon as we see or imagine the cue words.You can start by having small cue cards rather than writing down the whole presentation and opening in on the podium to refer. If you miss a particular sentence or fact, there is no need to get stuck and stop suddenly, just skip by mentioning that, the fact escapes my mind, moving on to the next point makes us get over this. Similar tips would be there for singing,dancing and playing instruments.