Sublime Text uses Hunspell for its spell checking support. Additional dictionaries can be obtained from the OpenOffice.org Extension List.
Dictionaries in a format ready to be used by Sublime Text are available at https://github.com/titoBouzout/Dictionaries.
Sublime Text currently only supports UTF-8 encoded dictionaries. Most dictionaries are not encoded in UTF-8, instead using a more compact encoding for the language in question. To use a dictionary with Sublime Text, it'll first need to be converted into UTF-8.
Once you have a UTF-8 encoded dictionary, it can be installed by placing it in a package, for example, Packages/User, which you can access from the menu item. Once the file is in place, you can select the dictionary from the menu.
There are two settings that effect the spell checking: spell_check, which controls if spell checking is enabled, and dictionary, which gives the path to the dictionary file to use. For example:
"spell_check": true, "dictionary": "Packages/Language - English/en_US.dic"
Added and ignored words are stored in the user settings under the added_words and ignored_words keys.