For this short little project, you will need:
- an AVR-based microcontroller like an Arduino or any of it's ilk. These instructions could probably be adapted to your MCU of choice.
- a DLO7135 dot matrix LED or other in the same family
- an 8-bit shift register like the 74LS164, 74C299, or 74HC594
- a breadboard
- hookup wire, wire cutters, etc.
A soldering iron isn't needed, although I use one later; you can get by without it.