I assume that you're referring to South Korea.
If you hold a UK passport can enter as a tourist for up to 90 days but you must have a ticket for leaving the country at the end of (or during) that period. You need a visa for all types of work, including teaching. You almost certainly need to obtain any work visa (either 'C-4' or 'E-2', as appropriate) before travel. (Most countries won't let you apply for an employment visa after arrival. Use the contact details, in my second link, to get a definite answer).
Foreign & Commonwealth Office:
http://www.fco.gov.uk...ntryRequirements&pg=4
Visa section of the South Korean Embassy:
http://gbr.mofat.go.k...iting/entry/index.jsp
Chris