Live sales can be very hectic at times. If you are relaxed you are likely moving too slowly. The people watching probably don't want to watch you search for your items or stand around saying "um" a lot. I try to prep for my live sales as much as I possibly can. Which is tricky if you are not completely sure what to expect.
For the miniatures sale I started off with my tripod all set up, with my clipboard of notes underneath. I had open, blank bags standing up, ready for name stickers or for me to write names on (if I didn't have a pre-made sticker). The sheets of name labels were off to the left. And all of my inventory was bagged and in order according to the PDF I posted last Monday.The extra Breyer items I found at the last minute were stacked on my pillows and my (dead) battery pack for my phone was waiting just in case. It died about 30 seconds into using it before the live and I could not find the correct charger to get it ready. I had a feeling I might need it.
Something new I tried this time around, to save time and a bit of money for myself, was to do just a couple of larger prizes for share prizes. Facebook gives you a list of everyone who has shared your stuff publicly. So right after the live ended (really, it was within minutes) I went to the list and copied the names into a random name chooser wheel. And I took a video of each choosing.