Cats hold their infants behind their heads with their mouth. We can also hold kittens easily in that way. But as they grow and gain weight, I don't think it remains proper way to lift. I usually hold the cats by their shoulder and lift like we lift a baby or child. Is it a proper way?
In my opinion the best way is to either carry them 'Lion King' style over short distances, or to gently grab them by the feet, and while enclosing your arms, to let the lay down on one of your hands, while you secure/pet them with the other.
My cats usually enjoy the lion king lift and offer little, to no resistance, which means they like it.
The other way is good but they sometimes resist. Probably due to heat issues.
You can also try carrying them around like babies. They also like that.
It's the "Don't"s that are more important than the "Do"s.
You should not lift a cat by the head, for obvious reasons.
You should not lift them by the tummy since they tend to overeat. Will you like someone to push you on the stomach after a visit to grandma?
By the tail, since it's a sensitive part, connected to the spine.
Hand around their neck, since you strange them.
By their feet, since they feel powerless and it's also painful, sometimes, for them.
If you avoid the "Don't"s you'll be OK.