For me, I take deep breaths and pretend for a few seconds that I don't care a bit about the fact that I finally have a shot. After all, I've sometimes waited years, months, all season or even just an hour for this one chance to finally take a shot on this animal. So if I pretend for a minute that it's no big deal, I usually calm down a lot.
Time helps me, though. Initially, it's exciting. On my little bear last year, I didn't see her until she was already within 20 yards. It couldn't have been more than 10 seconds before she was at 15 yards and pausing long enough for a shot. She had already turned her head to continue on and had taken a step by the time the arrow hit. I got edgy when she turned her head so I accidentally released before getting to full draw. Thankfully, the shot couldn't have landed better. I wish I had known she was so close before she appeared. Oh well. That's hunting.
I've taken more turkeys and shots at turkeys than anything else. Whenever the birds take more time to come in, when I can see or hear them coming in, I am MUCH more calm than when they appear suddenly and with a narrow window for a shot. Having that extra time to take a few deep breaths, collect my wits & be mindful of my shot cycle helps me a lot.