There’s another tab to the symbols dialog box: Special Characters. Here’s what that tab looks like:

The concept is the same: pick a character from the list and click Insert. Most characters also have a shortcut key assigned to them (as indicated in the character list); if you use certain special characters often it may be useful to memorize these shortcuts.

Most special characters (such as the copyright symbol, quotes, and hyphens) can be formatted and deleted just like regular text. You may need to enable document markings to see some other types of characters, such as spaces and breaks.