What we now know as the Gunpowder Plot began as a conspiracy between three men: Robert Catesby, John Wright and Thomas Winter. Only one of the three, Thomas Winter, survived to tell their account of the plot.
That account was extracted under torture, so we should approach it with come caution, but it is the best information that we have. His confession is examined in some detail in Thomas Winter's Confession and the Gunpowder Plot by the Jesuit priest, John Gerard.
While others would almost certainly argue with his conclusions, his examination of the confession is well worth reading in order to understand the controversies surrounding it.
Although the conspirators' main objective was to kill the King, targeting the State Opening of Parliament meant that they would also kill the King's nearest relatives, most of the Privy Council, most of the Protestant aristocracy, the senior judges of the English legal system, the bishops of the Church of England, and the members of the House of Commons. They hoped this would leave the state effectively leaderless.
Their next objective, had Parliament been destroyed, was to kidnap the King's daughter, the Princess Elizabeth who was then living at Coombe Abbey near Coventry. They planned to place Elizabeth on the throne as Queen, installing Henry Percy, the Catholic Earl of Northumberland, as Elizabeth's Protector (although they probably never told him of his expected role).
They intended that all this would have been accompanied by an uprising of Catholics within England, supported by troops and materiel from Spain. Whether Spain was aware of their expected role remains an unanswered question.
The UK Parliament website have some helpful resources about the 1605 Gunpowder Plot.
The UK National Archives have also made images of some of the primary source documents in their collection available as classroom resources on their website.
For more about the background to the Gunpowder Plot, and how the events unfolded, you might like to read The Gunpowder Plot: Terror And Faith In 1605 by Antonia Fraser.