You've been given lots of great advice, after 12 years I still get nervous too, but then I remember....I know how to do this, I do it all day everyday, my client doesn't, they are not judging every step I do, they're watching yes, but they are just interested, it's fascinating for them. I think sometimes we assume they are checking what we're doing, or trying to catch us out and they're really not. You might be new, but you know more than they do, and you know more than you think you do.
I have a couple of clients who have been with me since day 1, that's 12 years, coming once every 2/3 weeks, even now they don't know my manicure routine, they offer up palms instead of fingers when I'm ready to apply cuticle remover, they try to go and wash their hands too early before I'm ready for final buffing/polish, they need reminding to go and wash their hands but they watch everything I do and have done for 12 years, it just goes to show they're not really 'watching' they just looking and probably thinking about their own stuff like shopping, cooking, troublesome teenagers, work, or whatever. Yes they are expecting the best at the end but they're not judging how you get there, and they don't see the flaws we do, we're trained to look for faults, they just see pretty and cared for when we finish.
Think about how you would feel in their shoes, it's fine to tell them you are new and training but they need you to be confident, your confidence instills calm and reassurance in them. How would you feel if your tech was nervous and scared? It wouldn't make you feel comfortable, so fake it until you make it lovely