There are a number of sources of funding to support graduate study at Cambridge, at both Masters and doctoral levels. At the national level, the AHRC offers studentships that are open to both UK and other EU applicants, and cover tuition and maintenance costs (tuition only for non-UK applicants); applications are made through the University and we can help you with this. Click here for further information on the AHRC.
There are also various schemes specifically to support study at Cambridge. For UK and EU doctoral students there is the Cambridge Home/EU Studentships Scheme (CHESS). For students from outside the UK, the Gates Cambridge Trust offers full-cost support for all graduate degrees, while the Cambridge Commonwealth, European and International Trusts offer partial support for Commonwealth and non-Commonwealth students respectively, again at all levels. Finally the Cambridge International Scholarships Scheme (CISS) offers full-cost support for doctoral students from outside the UK.
Details of these and a number of other funding opportunities are available on the Graduate Admissions web pages. The Student Registry website includes an introduction to costs and funding and an overview of funding opportunities, with links to separate funding guides for UK, EU, and overseas students. Note that some of these schemes have quite early deadlines (for example October for the Gates Cambridge Trust), so you should begin researching funding opportunities at least a year before you intend to begin your course.