The civil service provides Ministers with several different types of support. As well as specialist policy teams, all departments have strategy and/or implementation units who help prepare and monitor departmental plans, always working closely with finance and human resources teams. And then there are communications teams as well as special advisers who provide political advice and support. Last, but not least, every Minister is provided with a small Private Office who help organise his or her diary and day-to-day communications within the department and wider government. This webpage provides links to sources of information about the way in which Private Offices work.
A short guide to working effectively with Private Offices is here.
More detailed but very readable advice is in Chapter 2 of Christopher Jary's Working with Ministers.
An amusing - but also essentially accurate - speech by ex-Private Secretary Edward Bowles is here.
And this Private Office Handbook will give you a feel for the atmosphere within, and working practices of, a Private Office in the early 1990s. Much of the advice in the handbook will apply equally well today, although some of the detail is of course out-of-date.
In particular, some departments have introduced Extended Ministerial Offices which bring together the traditional private offices, special advisers and external appointees to provide a much wider range of support functions. The relevant Cabinet Office guidance is here. Further background to this somewhat controversial development is here.