(Please try not to suggest putting the fish in quarantine tanks)
Put the fish in a quarantine tank.
In 40+ years of doing this I can't recall a single acclimation process issue causing me to lose a fish, and I have done every one of the suggested methods on this thread. It barely seems to make a difference as far as I have experienced.
Put a healthy fish into a healthy tank with a quick temp acclimation and a few minutes exchanging water *while watching for a reaction or lack thereof* and you are good to go. I've just dropped plenty in as well depending on the situation with no issues.
What I have seen is resident fish getting all over new arrivals and stressing them to death in short order.
I'm not saying you have to medicate, do the 40 day thing, or even do this every time. However, if you are adding a fish to a tank with plucky residents, a quarantine tank can be your best friend.
Give new arrivals some time alone, get them eating and make sure the fish has fully recovered from transit. I can then pick a time, at my leisure, when I am going to be home to watch the tank for a few hours. I will then observe how it's going, and have time to react if things go south.
I keep an acclimation box handy as well, and will start the new arrival out in one if I feel it's needed. The acclimation box and spare tank also give me two options ready to go if the introduction is not going well...
This, more than anything else I have done, has made quick losses of new fish almost nonexistent for me.