First off, this article assumes that you are using a spell check capable browser such as Firefox.  If there is another browser with spell check, then go for it.

The problem I run into with these FCKeditors is that there is an option to spell check the document, but the option is grayed out.  Also, the Firefox spell check does not work within the editor.  So, you have a few options here.  1) Type your document in a word processing application and then copy paste it into the editor.  2) Select Basic Text Box instead of Rich Text Editor.  3) Select Source once you are done typing.

Option 1 is ok and may be the preferable method for long documents.

Option 2 is no good as it is just a text box, and switching over to it after you are done typing may cause some loss in formatting.

Option 3 is the best method.  Just select Source and right-click on any underlined words, that are not HTML code, and select the correct spelling for the word.  An example is shown below.