Use :set spell to turn on spell-checking.
:help spell will give you all the details.
Here are some excerpts:
To search for the next misspelled word:
]s Move to next misspelled word after the cursor.
A count before the command can be used to repeat.
'wrapscan' applies.
[s Like "]s" but search backwards, find the misspelled
word before the cursor.
Finding suggestions for bad words:
z= For the word under/after the cursor, suggest correctly
spelled words.
To add words to your own word list:
zg Add word under the cursor as a good word
To remove words from your own word list:
zw Like "zg" but mark the word as a wrong (bad) word.
I don’t put :set spell in my .vimrc because when I’m coding there are just
too many variable names in my comments that get flagged.
If there is a certain file type you want checked use an auto-command in your .vimrc.
Or just turn it on manually when you need it.
Use :set nospell to turn off spell-checking.
Use :set spelllang=en to change the language used in spell-checking.
Also see :help set spelllang for information on changing your dictionary to
include other regions, languages, or word sets.