By default, Firefox spell-checks what you type when typing into multiple-line text boxes. Misspelled words are underlined in red. To correct a word, right-click it and select the correct spelling from the context menu. You may also add the word to the dictionary, if it is correct.
To change or add a dictionary, right-click anywhere in a multi-line text box and select the appropriate option from the context menu. Here you may also disable spell-checking for this text box. If you want to globally disable spell checking, open the Preferences window as described in Section 13.7.1, “Preferences” and go to the category Advanced. Deactivate Check My Spelling As I Type.