What I always do is copy-paste to and from a text editor like notepad.
If you are on a PC, just use Character Map with the font chosen, to select from the full set of characters. Copy/Paste, as Joe points out. I am sure that there is something similar on a Mac, but do not know what it would be.
Many wordprocessors have direct access to a lot of different characters. In WordPerfect, it's Ctrl-W, with a drop-down for dozens of symbols, etc.. Again, Copy/Paste.
One can usually use the Alt+___ for the numeric value of the character. Be sure to use the numeric keypad, and not the numbers at the top of the QWERTY keyboard. For instance, Alt+128 = Ç.
In Titler, one can access many different characters. This article goes into more detail: http://forums.adobe.com/message/3702803#3702803