EU citizens can live and work in the UK free of immigration control and don't need a visa to enter the country.
All other nationalities should contact their nearest British diplomatic mission to obtain a visa. Six-month/one-year multiple-entry visas cost from £50/85.
To extend your stay in Britain contact the Home Office, Immigration and Nationality Directorate (0870 606 7766; Lunar House, 40 Wellesley Rd, Croydon, London CR9 2BY) before your existing permit expires. You'll need to send your passport with your application.