Like most word processing software worthy of the name, Google Docs includes a spellchecker that lets you check over your documents and hopefully catch and correct any spelling errors before you go public.
When the spellchecker finds a word it believes to be incorrect, it will underline it; you then have the opportunity either to correct the spelling, or to add that word to your custom dictionary.
To add it to your dictionary, right-click on the word in question and select the appropriate option from the menu:
To manage the words in your personal dictionary, use Tools > Personal dictionary… from the menu. Here you can add and also (a recently introduced feature, and long overdue) delete words from your custom dictionary.
Unfortunately, you can’t currently have more than one custom dictionary, as you can in some other packages such as MS Word.