The Order of the Golden Dawn was formally established in 1888, though much preparatory work, including the deciphering of the Cypher Manuscript (which is open to some scholarly debate) and the writing of the rituals was conducted the year before.
There were three founders of the Order: Samuel Liddell MacGregor Mathers, William Wynn Westcott and William Robert Woodman. Together they created an Order that attracted some of the Victorian era's cultural elite.
Samuel Liddell MacGregor Mathers
Mathers was of poor means, and struggled financially for much of his life, despite the support of others in the Order. He devoted much of his time to his studies and magical pursuits, and was often found in the British Museum, where, indeed, he met some of the Order's initial members, including his future wife Mina (later Moina) Bergson.
Mathers started his esoteric pursuits with Freemasonry, and then joined the Societas Rosicrucian in Anglia (SRIA), as well as the Hermetic Society run by Anna Kingsford (in which he and Westcott were prominent members), and the Theosophical Society run by Madame Blavatsky.
In addition to the substantial volume of material he created for the Order, some of which remains unpublished, Mathers wrote several books and translated several important occult texts, including The Key of Solomon the King and The Book of the Sacred Magic of Abramelin the Mage, which remain influential to this very day. He also contributed numerous articles to occult journals, including a lengthy series on Iamblichus for Anubis.
Arguably an eccentric figure, Mathers faced rebellion by some of the Order's members towards the end of the 19th Century, and continued the work of the Order under a new name. He died in 1918, allegedly of Spanish influenza, and appointed John William Brodie-Innes (motto: Sub Spe) as his successor.
Mathers took several mottos in the Order, including 'S Rioghal Mo Dhream ("Royal is my tribe"), borrowed from the MacGregor clan, to which he claimed links, and Deo Duce Comite Ferro ("With God as my leader and the sword as my companion").
William Wynn Westcott
Westcott was the organisational force behind the Order, helping both in its foundation and the subsequent day-to-day running of it. He ensured examination protocols were followed, but he also contributed significantly to the teachings of the Order.
He claimed to have stumbled upon the Cypher Manuscript, and received letters from one Fraulein Sprengel, granting permission to him and Mathers to found a temple in London. Much of these claims have later been disputed by historians, and remain the subject of considerable debate.
Westcott was a member of numerous esoteric organisations, with a particular interest in the fringe rites of Freemasonry, and, indeed, held prominent positions in many of these, leading A.E. Waite to say that he was the British custodian of many obscure rites (see here), such as, for example, the Swedenborgian Rite. He was also a member of the Quatuor Coronati research lodge, and took over as Supreme Magus of the SRIA when Woodman died.
Westcott translated several influential texts, including the Sepher Yetzirah and the Chaldean Oracles of Zoroaster, both of which became part of the Golden Dawn's teachings.
Westcott was a Crown Coroner, and it was this occupation that ultimately forced him to resign from the Order in 1897, when he accidentally left some papers in public view. He continued his work privately with members, and held office in other esoteric organisations until his death in 1925.
Westcott took several mottos in the Order, including Sapere Aude ("Dare to be wise"), and Non Omnis Moriar ("I shall not wholly die")
William Robert Woodman
Woodman was Supreme Magus of the SRIA at the time of the Golden Dawn's founding, and this was an important organisation to which Mathers and Westcott also belonged, contributing its grade structure, among other things, to the Order.
According to Westcott's claims for the foundation of the Order, Mathers proposed that Woodman be selected as a third chief because of the requirement for three chiefs in the Cypher Manuscript, and he was appointed the role of Imperator, ruling the Order. This appears to have been largely a ceremonial appointment, and was likely designed to give greater credibility to the Golden Dawn, given Woodman's prominent position elsewhere.
Woodman died in 1891, before the formation of the Second Order, and left behind surprisingly little to tell us of just what he did in those early years of the Order. In Westcott's brief lament for Woodman's death in the Historic Lecture, he talks more about his role in the SRIA than the GD.
It appears that Woodman never wrote any lectures for the Order, though his papers for the SRIA do show he was well-versed in the Qabalah.
Woodman took several mottos in the Order, including Magna Est Veritas Et Praevalebit ("Great is the truth and it shall prevail") and Vincit Omnia Veritas ("Truth rules all").