First you load LOADER.TAP from SpecAY. Once that is loaded just select the .AY file you want to load and away you go.
You can download version 1.5 of the firmware from Here.
You can download Luca's original version of the firmware which is for an Arduino Mega with LCD and buttons shield from Here. Interestingly Luca has added a filesize counter with his firmware so that you can see how large the file currently selected is.
You can watch a video of Luca's TZXDuino at work here.