Apart from some hardware issues with the FabISP, this weeks assignment of programming a board with an LED to blink repeatedly, or light up when a button was pressed/not pressed was relatively straightforward. I followed several different tutorials, and modified pre-existing example code in the Arduino IDE.
The ATtiny 44A datasheet  was a good reference. The C-book was also highly recommended, available here , and here in a less formatted version (in case the first link does not work).
I also needed to download the ATtiny hardware  to my Arduino library, as explained in the high-low tech tutorial.