Nationals of countries in the European Economic Area (EEA) and Switzerland can live and work in the UK without requiring any form of authorisation.
For non-European nationals, the UK operates a points-based system of immigration which is comprised of five tiers. The vast majority of non-European workers who intend to work in the UK fall under Tier 2, the category for skilled workers who have received a job offer.
Employers who wish to offer a job to a migrant worker must act as their sponsor during their stay in the UK (unless they are coming here for six months or less in certain circumstances). But a sponsor licence must be obtained before sponsoring a migrant. The UK Borders Agency provides a checklist (see link, below) to help employers decide whether they are eligible to apply for a sponsor licence under the points-based system.
Sponsor Application Checklist