Cruise ship passengers leaving the same day do not require a visa. 

For longer visits visas are not required by visitors from Andorra, Argentina, Australia, Austria, Belgium, Bulgaria, Brazil, Canada, Chile, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hong Kong, Hungary, Iceland, Ireland, Israel, Italy, Japan, Korea (Republic), Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Netherlands, New Zealand, Norway, Paraguay, Poland, Portugal, Romania, San Marino, Slovakia, South Africa, Spain, Sweden, Switzerland, Tawain, United Kingdom, United States, Uruguay, Vatican City.

Visas can be obtained from a British embassy

Falkland Islands tourist information