There is no answer to this question. It is like asking "How long does it take to learn to play the piano?"
I have worked with people that 'figured' horses out in a few months and had so much natural ability that I could offer a little coaching and they were getting all kinds of things right, almost from the git-go. I have worked with other people that have spent years struggling to just keep horses from going down-hill from the first time they touched any horse's lead or reins. They could not live long enough or try hard enough to ever learn to teach one much of anything positive.
I think it all depends on how much natural feel a person has. Some people are born with more natural timing and feel than others can develop in a lifetime. I think about anyone can develop a good degree of ability to handle and ride trained or well-started horses. The timing and feel it takes to train one right is, in great part, A GIFT.
I think the best way to learn is to go to work for a trainer that one respects or at least have a very accomplished horseman (or woman) for a mentor. The few people that can just do it on their own are rare and many horses will suffer from their trial and error methods. After all, you would not try to teach yourself how to fly an airplane. People should not try to invent horse training over when there are people that have it down pretty pat.