The spell-checker continuously checks all words that you are typing. If you make a typo or a word is not in the dictionary it will be underlined red and look like this:
In this case 'Robrets' was typed instead of 'Roberts'. Right clicking on the underlined word will open a context menu:
The context menu includes a list of suggestions. In this case the correct spelling 'Roberts' is shown and can simply be applied by selecting it.
If the correct spelling is not in the list of suggestions you can copy the word to your clipboard and search for it on Google for example.
The spell-checker also gives you an option to add an unknown word to the dictionary, so it won't be underlined anymore in the future.
Please note that the dictionary works system-wide (all users have access to the same dictionary), so any new words will become available to all users. New words will be accepted into the dictionary after being reviewed internally.