Obviously if one gets an E on the required N.E.W.T.S. then you'll go to Mungo's to train, but how long does it take to get to become a healer?
There's no canon source that puts a definitive number on it, as far as I'm aware. The recruitment materials seem to focus on the admission requirements rather than the length of training.
"Well, I don't fancy Healing," said Ron on the last evening of the holidays. He was immersed in a leaflet that carried the crossed bone-and-wand emblem of St Mungo's on its front. "It says here you need at least "E" at N.E.W.T. level in Potions, Herbology, Transfiguration, Charms and Defence Against the Dark Arts. I mean...blimey...don't want much, do they?"
(Order of the Phoenix, Chapter 29, Careers Advice).
It is true that there's a period of post-Hogwarts training that's required before you can attain the rank of Healer. During this training you are called a Trainee Healer.
'Dangerous' Dai Llewellyn Ward: Serious Bites. Underneath this was a card in a brass holder on which had been handwritten: Healer-in-Charge: Hippocrates Smethwyck. Trainee Healer: Augustus Pye.
(Order of the Phoenix, Chapter 22, St Mungo's Hospital for Magical Maladies and Injuries).
We know that Trainee Healers can be pretty young.
"Well - now don't get upset, Molly, but Augustus Pye had an idea...he's the Trainee Healer, you know, lovely young chap and very interested in...um...complementary medicine...
(Order of the Phoenix, Chapter 23, Christmas on the Closed Ward).
That's really all the information we have on the subject. Judging by Pye, you can become a Trainee Healer at a very young age - probably straight out of Hogwarts if you have the right grades. You then learn on the job under the guidance of a more experienced Healer. There's no detail given about how you earn your stripes or how long it takes to become a full Healer.