Summarizes what I always refer to in http://vimdoc.sourceforge.net/htmldoc/spell.html.
To spellcheck in Vim type:
:setlocal spell spelllang=en_us
To correct the spelling of a word use:
]s Move to next misspelled word after the cursor.
[s Like "]s" but search backwards z= For the word under/after the cursor suggest correctly spelled words
Other resources: Jake Harding has a good write up on "Using Spell Check in Vim" here: http://thejakeharding.com/tutorial/2012/06/13/using-spell-check-in-vim.html.