So being a "Doodler Extraordinaire", I've done a variety of "doodlin' gigs" - one of them being caricatures.
I've been caricaturing now for a good 5.5 years now and I can say both my confidence and ability have grown quite much since my start.
One of the things that has been a constant since the very beginning has been "the staring".
"The Staring" is when the person you're drawing decides to stare intently into your pupils while you are drawing them.
This kind of staring can be distracting- instead of studying the distance between this person's ears to eyes to nose, or getting the proportions of the forehead, your gaze is drawn into their eyes- and it just makes the process longer, and you (or at least I) more anxious.
-One way I've gotten around this is giving an initial explanation of what I'll be doing and instructing the client to focus on any point behind my head- and just to be comfortable.
Doing so has helped me out GREATLY, and 9 times out of 10, there's no other problems that arise from this.
Now, there are those special people and/or gigs where no matter what I say- these people are set on making me look at them...or want to look deep enough into my eyes they see the essence of my soul- whatever the case, in those situations you just have to go with it and get the job done as quickly as possible.
I find I run into this situation more when I'm doing group caricatures (anywhere from 2 to 5 people)- its like, collectively, people decide not to follow the instructions and just stare at me...to any caricaturist starting out, my advice is just to be confident and have fun with your work- there's only so much you can control.
--One other skill that I'd say is pretty essential to being a caricaturist is the ability to socialize. Generally, caricaturists are pretty fast drawers- but no matter how fast you are, sitting still for one minute can feel like an eternity if the person is not engaged in conversation or actively doing anything.
Think about when you get your haircut. Your barber/hair stylist, 4 times outta 5, will at least attempt to engage you in conversation. Not to say you're not an interesting person, but the actual conversing takes your mind off of your hair cut....making it easier for your hair cutter to get his/her job done, as time seemingly goes faster- provided you are having fun conversing.
-This theory/social diversion is used in a variety of jobs - one of them being caricaturing. I've even discovered that those people who refuse to look at anything but me will finally relax their eyes and turn away once I get them engaged in a conversation- because now they are focusing on the conversation vs the drawing, I can then myself concentrate moreso on my work and relax.
Yes, drawing someone while determining what features to emphasize while simultaneously engaging in a conversation can be quite the multi-tasking job, especially if you are caricaturing a group of people- but take it from someone who had anxiety attacks before getting to a gig: have confidence in what you are doing, practice a lot, and you'll get there before you know it.