Editing my post, Google just released the Personal Dictionary. Once I see documentation in the support files I will post.
In your Google Doc, go to Tools > Personal Dictionary and all of your spelling additions will be stored there. You will be able to add or remove custom words.
To add a word, right click the underlined word and select Add to personal Dictionary.
To remove the word, right click the word and select Remove from Personal Dictionary.
Again, this is brand new to Google Docs and once I have a support file I will post it here.