1) Be qualified to perform a 'shortage' occupation - shortages include social work, nursing (including certified nurse midwives, anethetists, and nurse practitioners), radiography, ultrasonography and other forms of nuclear medicine, physicians, dentists (not dental hygienists, but dentists), some areas of teaching (such as secondary level maths and sciences), etc.
2) Be married to an EU or UK national
3) Be a full-time student (in which case you are restricted to working 20hrs/week during term times and full-time at term holidays) or the spouse of a full-time student - in which case there are no restrictions on the amount of hours you work
4) Have a British parent - although restrictions apply depending on your year of birth.
5) Have an EU national parent
6) Hold Commonwealth nationality
7) Be a recent university graduate - in which case you may be eligible for a BUNAC visa which will allow you to work in certain occupations for 6 months
8 Find an employer willing to sponsor a work permit for you and be able to successfully obtain a work permit on your behalf