The University College, London Constitution Unit has a wealth of valuable information on its website.
In particular, the Unit’s guide to Being a Special Adviser contains some very good advice for newly appointed (or about to be appointed) SpAds. It can be found here.
Equally useful are the Unit’s videos of short interviews with former SpAds and their Secretaries of State.
Last, but certainly not least, the Unit has published Special Advisers: Who they are, what they do and why they matter (Ben Yong and Robert Hazell, Hart, August 2014), including a chapter by David Laughrin quoted elsewhere in this section of this website. This book is a must-read comprehensive study of Special Advisers, from a wide range of viewpoints.
Nick Hillman and the IfG published this very perceptive report in March 2014: In Defence of Special Advisers: Lessons from Personal Experience.
And Mark Madden has published Generals, Troops and Diplomats - highly readable induction material for advisers within the Australian political system.
Earlier more formal documents about Special Advisers include the Sixth and Ninth Reports of the Committee on Standards in Public Life which were published in January 2000 and April 2003. (The SpAds chapter of the Sixth Report is here, and the Ninth Report is here.) Both made a number of recommendations about, amongst other things, Special Advisers, and the ninth report recommended that Special Advisers should no longer be temporary civil servants, and set out what a special adviser must not do and the kind of things they can be allowed to do.
The Government's response to the sixth report was published in July 2000. The Government said that it intended to continue to conform closely to the guideline that there would be a limit of two Special Advisers per Cabinet Minister, except in special circumstances (e.g. if advisers are brought in on the basis of their particular expertise). The Government went on to say that it had made it clear when it was elected that it intended to strengthen the centre of Government. It had therefore expanded the No. 10 Policy Unit and created a Strategic Communications Unit and a research unit, staffed by a mixture of permanent civil servants and Special Advisers, who do not count against the 2/Cabinet Minister limit. It had no plans to further expand these units, but believed that they had been valuable developments.
Sir Richard Wilson, then Head of the Civil Service, delivered an interesting speech in 2002 (Portrait of a Profession Revisited) dealing with the role of Special Advisers, the need for a Civil Service Act and so on.
It is also worth reading this note of an October 2003 Public Administration Committee conference on the future of the Civil Service, which included references to SpAds.
The IfG published an interesting report and commentary in late 2020.