If you aren't an EU citizen or visiting a family member, then you probably need to apply for a tourist visa. This will normally be valid for up to 6 months. In order to be sure that a visa (rather than another form of entry clearance) is what you need, you can fill out this questionnaire if you like.
The process of getting a visa depends on where you come from - for example, certain European countries, such as Switzerland, have a different kind of entry requirement. You can learn more here.
You can apply from a UK visa application centre in any country. You can find information on this through the pages mentioned above, or if you put 'UK tourist visa' plus the name of your country or nearest big city in a search engine, you should be able to find your centre that way. Your centre will tell you the exact requirements for your nationality and situation; if there are any problems, you should contact the UK Border Agency.