After clicking on the "Check Spelling" button at the bottom of the page, every word you entered into a text field is compared to the words in a dictionary. Words that are not found in the dictionary are placed into little text fields, possibly with suggested corrections next to them. If one of the corrections fits, just click on it to copy it into the text field. Otherwise, you might have to manually correct the text. Once you are done, click on "Finish Spell Check" to return to the previous view where all text is editable.
If the spell checker finds no errors, there will be no editable text. In this case, just click on the Finish button.