As I recall, what we did was add a reference to the Word assembly in our project.
Then, and this is entirely psudo-code-type-stuff, we did something like this:
1. Passed each word into Word's spell check object
2. If there were suggestions, we'd display those to the user and if they selected one we'd replace the original text.
I know that sounds over-simplifying it, but that's pretty much what it was. It was a while ago, and can't remember how much code there was to do it, but I don't think it was a huge amount.
D