No set method overhere. Every singer is different. Some do full takes, some do verse/chorus... Mostly though I do 2-4 takes and use the best one and replace/retrack some parts that can be better.
After that I have no problem doing a little autotune. If it is sung good enough, in a couple of minutes we have the tuning fixed and it is inaudible with most singers after that...
It's more of a safety net and by showing inexperienced singers early on what can be done with autotune, they relax a little bit on the "in tune singing" and lets them focus on there performance.
Nothing worse than a singer that is completely stressed about nothing else than pitch