Where can I find an example of reading from and writing to the TINI Board's 1-Wire busses?
Check out the MailTemp program in the examples directory included with the TINI firmware distribution. This is a very simple program that examines the temperature from a DS1820 or DS1920 temperature sensor, but it´s a good way to get started.
There are several other examples in this same directory. The FindiButtonsConsole example is another simple one which enumerates all the 1-wire devices attached to the TINI.