I have issues talking in front of crowds or
in front of class (stage fright, pretty much)
In my experience, stage fright, once learned, tends to not go away. It is, however, much like getting into cold water. The
anticipation is usually much worse than the event itself. Sitting in your desk for 20 minutes...waiting and dreading for the teacher to call on you...the growing fear each time one student delivers a presentation, knowing that sooner or later it will be your turn...that anticipation is much worse than the speaking itself.
Once you jump into the pool the anticipation is gone. Once you get up and start speaking, the anticipation is gone. There's no more reason to dread or anticipate it.
Simple solution: ask to go first. In this way you minimize the time spent dreading the future. This also promotes learning to dread it less, since experience will be a short period of anticipation and dread rather than a long one. It's easier to be less afraid of something that's painful for a short while than something that's painful for a long time. Minimize the time you spend waiting to speak.
On stage rather than in a classroom, this usually isn't an option. But as a simple, practical matter...one can choose to avoid situations where one is likely to go on stage.
and with explaining ideas
In my experience, this is usually that the person doing the explaining doesn't understand what they're explaining as well as they think they do.
trying to convey vague ideas to a million pairs of eyes.
Exactly. If the idea is
vague to you, then that lack of clarity is likely to come through in your expression. It's sometimes easier to do than to know or explain. Anyone can turn on a light switch. But that ability does not indicate sufficient familiarity to explain
why a light switch works.
Simple solution: clarify to yourself in advance what it is you'll be explaining. Sit down in a quiet room and explain to yourself out loud, in full detail, how whatever it is you'll be explaining works. Pretend that you know nothing about what you're explaining, and go through the act of explaining to yoruself. Ask yoruself questions. Don't allow yourself to fall back on personal experience as shortcuts in the process.