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I'm going to assume that by "teaching" you mean "how did what is taught come to be known and understood" rather than this being a question about teaching methods.
The teachings have their source in a man named Siddhartha who set out to relieve the suffering in the world. He studied with the great religious leaders of his time and was unsatisfied with what they taught, so he devoted himself to finding his own way. Much of what he arrived at had its origins in the methods of his time (for example: meditation) or was a reaction to what he felt was wrong with the methods of his time (his famous Middle Way is a rebellion against the ascetism and indulgence of the time).
Rather like Columbus was not the first to "discover" America but was actually the last to discover it -- and afterwards it stayed discovered -- the Buddha may not have been the first to come up with the answer he did, but he is the only one who found the seed, planted it, nurtured it, made it grow, encouraged it to multiply, and got it to take root in the world once and for all. For all intents and purposes it's simplest to say he was the first:
He was the first to come up with a really good answer to the question: Why are we humans so miserable and what can we do about it? His answer is both very simple and very deep and difficult to get a good grip on. We've got one way of looking at the world and ourselves in the world deeply ingrained in our thinking and seeing it another way is the first challenge and then knowing it through and through is the rest of the challenge. The methods support coming to the deeper understanding of what the Buddha saw, the problem and the cure for the anguish we cause ourselves.
So the truest answer to "how did the teachings develop" is through the persistence, insight, and practice of one man 2500 years ago. There have perhaps been a few people since who have had some skill at adding to methods, or clarifying ways to put the teachings so that they will be easier to understand, but the truth at the center of it is the same now as it was then -- it needed no development once found.
This is all wrong don't listen to it at all
What else can I help you with?
Where did buddism develop?
Buddhism developed in Nepal / Northern India around 500BCE based upon the teachings of The Buddha, Siddhartha Gautama.
How was Buddhism started?
Buddhism grew from the teachings of Siddhartha Gautam, the Buddha (hence BUDDHism). Some of his main teachings were karma, the Four Noble Truths and the Eightfold Paths.
What is the religion on the teachings of siddhartha?
Buddhism
How did Buddhism develop into faith?
Buddhism is still today a very broad church with a range of views and ideas all coexisting under the umbrella term 'Buddhist'. Not all of these have a devotional or faith based approach. When talking about faith in Buddhism it is important to make a distinction between those Buddhists that have faith: in the Buddhist teachings, in the experiential reality exposed by the teachings and neither of the above.
Who was the historical leader of Buddhism?
Siddhartha Gautama is the Buddha and the founder of the teachings that comprise Buddhism.
What are 4 different types of Buddhism that develop in Japan?
pure-land buddhism zen buddhism buddhism ??
What is Buddhism's founder called?
Buddhism is a variety of beliefs and practices based on the teachings of Siddhartha Gautama
What is the riligios symbol for Buddhism?
The religious symbol for Buddhism is the teachings of the Buddha or the Three Noble Jewels.
How did popular Buddhism compare with original Buddhist teachings?
I am assuming that what you are asking is how does Buddhism today compare to what the Buddha taught. Buddhism over the years has been enriched by each culture that has been exposed to; changing the nature of practice just slightly each time. So Chan Buddhism (China) is slightly different in practice then is Zen Buddhism (Japan, Korea). But the teachings have always remained the same. Now when I speak of practice, it is the methods used to teach the Dharma (the teachings). The biggest change in Buddhism since the Buddha is the development of Mahayana Buddhism. Mahayana Buddhism, to which is the tradition I practice, added teachings from later Buddhas and Bodhisattvas to The Buddha's original teachings in regards to living a compassionate life to help all other beings. So Buddhism adapts the methods but never the message or teachings.
How many different versions of Buddhism are there?
There are really only 2 distinct types of Buddhism, though there are subgroups to them. The two major groups are Theravada and Mahayana. Theravada is call the "teachings of the Elders" and is most closest to the original teachings of the Buddha. Mahayana incorporates teachings of later Buddhas and Bodisatvas into the Buddhas original teachings. All the differnt lineages of Buddhism fall within one of these two groups but all teachings agree as to what the Buddha taught and to what the objective of Buddhism is.
Whose teachings formed the bases of Buddhism?
Siddlartha
What religion follows the teachings of Gautama Buddha?
Buddhism
