Here's how to do spell checking in Apple's Safari Browser:
Go to the Edit menu and navigate to the Spelling sub-menu. Here you can invoke the spell checker as needed using the command+; keystroke combination. But even better, you can turn on permanent spell checking capabilities with the 'Check Spelling as You Type' menu item.
Note: If these menu items are grayed-out and not selectable, then you need to go to a page with a form and put the cursor into a text area of the form and then turn on the 'Check Spelling as You Type' menu item.
Now every text area on each web page within your browser will be spell check enabled. You will see a curly red line underneath each word that the OS X spell checker does not recognize. You can then invoke the spelling options menu with command+: or use the menu option seen above.
Thanks to
Eric Bailey's .Mac Blog for the instructions.