The tale of Vortigern and the Dragons comes from Nennius and the Historia Brittonum Chapters 40, 41, and 43. Although a near identical version appears in Geoffrey of Monmouths's Historium Regnum Britanniae except that the character of Ambrose or Ambrosius Aurelianus is replaced by that of Merlin presumably because it offerered a better fit to his essentially fictional narrative.
The same tale also gets recycled in more modern guises under the title "Why the dragon is the symbol of Wales" or something similar, which it isn't. The dragon was essentially a Roman emblem adopted by early Welsh kings such as Cadwallon ap Cadfan as their battle standard, and similarly adopted by later leaders who sought to appeal to Welsh nationalistic aspirations such as Owain Glyndwr and even Henry Tudor.
Essentially the tale consists of a prophecy to the Welsh that "our people shall rise and drive away the Saxon race from beyond the sea, whence they originally came" and bears the same message as the poem Armes Prydein Vawr and the prevailing notion that Arthur would one day return to lead his people to victory.
The Historia Brittonum relates the events after the decision made by Vortigern, the Romano-British king to hire some Jutish mercenaries.
But soon after calling together his twelve wise men, to consult what was to be done, they said to him, "Retire to the remote boundaries of your kingdom; there build and fortify a city to defend yourself, for the people you have received (1) are treacherous; they are seeking to subdue you by stratagem, and, even during your life, to seize upon all the countries subject to your power, how much more will they attempt, after your death."
The king, pleased with this advice, departed with his wise men, and travelled through many parts of his territories, in search of a place convenient for the purpose of building a citadel. Having, to no purpose, travelled far and wide, they came at length to a province called Guenet (2); and having surveyed the mountains of Heremus (3), they discovered, on the summit of one of them, a situation, adapted to the construction of a citadel. Upon this, the wise men said to the king, "Build here a city; for, in this place, it will ever be secure against the barbarians."
Then the king sent for artificers, carpenters, stone-masons, and collected all the materials requisite to building; but the whole of these disappeared in one night, so that nothing remained of what had been provided for the constructing of the citadel. Materials were, therefore, from all parts, procured a second and third time, and again vanished as before, leaving and rendering every effort ineffectual. Vortigern inquired of his wise men the cause of this opposition to his undertaking, and of so much useless expense of labour? They replied, "You must find a child born without a father, put him to death, and sprinkle with his blood the ground on which the citadel is to be built, or you will never accomplish your purpose."
In consequence of this reply, the king sent messengers throughout Britain, in search of a child born without a father. After having inquired in all the provinces, they came to the field of Aelecti, in the district of Glefesing (4), where a party of boys were playing at ball. And two of them quarrelling, one said to the other, "boy without a father, no good will ever happen to you." Upon this, the messengers diligently inquired of the mother and the other boys, whether he had had a father? Which his mother denied, saying, "In what manner he was conceived I know not, for I have never had intercourse with any man;" and then she solemnly affirmed that he had no mortal father. The boy was, therefore, led away, and conducted before Vortigern the king.
A meeting took place the next day for the purpose of putting him to death. Then the boy said to the king, "Why have your servants brought me here?"
"That you may be put to death," replied the king, "and that the ground on which my citadel is to stand, may be sprinkled with your blood, without which I shall be unable to build it."
"Who," said the boy, "instructed you to do this?"
"My wise men." answered the king.
"Order them here," replied the boy; this being complied with, he then questioned them. "By what means was it revealed to you that this citadel could not be built, unless the spot were previously sprinkled with my blood? Speak without disguise, and declare who discovered me to you."
Then turning to the king he said, "I will soon tell you every thing; but I wish to question your wise men, and for them to disclose to you what is hidden under this pavement." They acknowledging their ignorance, "there is," said he, "a pool; come and dig:" they did so, and found the pool.
"Now," he continued, "tell me what is in it." But they were ashamed, and made no reply.
"I," said the boy, "can discover it to you: there are two vases in the pool." They examined, and found it so: continuing his questions, "What is in the vases?" They were silent.
"There is a tent in them," said the boy; "separate them, and you shall find it so." This being done by the king's command, there was found in them a folded tent.
The boy, going on with his questions, asked the wise men what was in it? But they not knowing what to reply, "There are," said he, "two serpents, one white and the other red; unfold the tent;" they obeyed, and two sleeping serpents were discovered.
"Consider attentively," said the boy, "what they are doing."
The serpents began to struggle with each other; and the white one, raising himself up, threw down the other into the middle of the tent and sometimes drove him to the edge of it; and this was repeated three times. At length the red one, apparently the weaker of the two, recovering his strength, expelled the white one from the tent; and the latter being pursued through the pool by the red one, disappeared.
Then the boy, asking the wise men what was signified by this wonderful omen, and they expressing their ignorance, he said to the king, "I will now unfold to you the meaning of this mystery. The pool is the emblem of this world, and the tent that of your kingdom: the two serpents are two dragons; the red serpent is your dragon, but the white serpent is the dragon of the people who occupy several provinces and districts of Britain, even almost from sea to sea. At length, however, our people shall rise and drive away the Saxon race from beyond the sea, whence they originally came; but do you depart from this place, where you are not permitted to erect a citadel. I, to whom fate has allotted this mansion, shall remain here; whilst to you it is incumbent to seek other provinces, where you may build a fortress."
"What is your name?" asked the king.
"I am called Ambrose" returned the boy.
"What is your origin?"
"A Roman consul was my father." he replied. Then the king assigned him that city, with all the western provinces of Britain; and departing with his wise men to the sinistral district, he arrived in the region named Gueneri (5), where he build a city which, according to his name was called Caer Guorthegirn (6).
(1) The people you have received being the Germanic mercenaries Vortigern or Anglo-Saxons if you prefer.
(2) Guenet is obviously Gwynedd
(3) The mountains of Heremus are now better known as Snowdownia
(4] Supposedly Bassalig in modern Gwent.
(5) Presumably Gwent
(6) Or the fortress of Vortigern, Guorthegirn being a more direct anglicised version of Gwrtheyrn