How do I add words to the OS X user dictionary?
Right click on the word and choose Spelling and Grammar from the list. Then select Show Spelling and Grammar.

You'll see the option to "learn" the word (see picture).



The learned words are stored in ~/Library/Spelling/. ~/Library/Spelling/LocalDictionary applies to all languages and for example ~/Library/Spelling/en only applies to U.S. English. When you press the learn button, the word is added to ~/Library/Spelling/LocalDictionary if the spelling language is set to automatic or to ~/Library/Spelling/en if the spelling language is set to U.S. English. 

If you edit the files in ~/Library/Spelling/ directly, you can apply the changes by terminating the AppleSpell process. Just quitting and reopening applications does not apply the changes.