First, install the micro SD card into the Raspberry Pi Zero. Then, plug in the HDMI cable to a monitor or TV. You will need to use the mini HDMI side of the cable on the Raspberry Pi Zero, and the full size HDMI for your TV or monitor. Now, use the included power adapter and plug it in to the 'PWR IN' port on the Raspberry Pi Zero.
You should see it almost instantly start to boot up into the RetroPie system. Give it plenty of time to fully boot up and you should be able to scan through all of the available emulators and we have included some free games to get you started.
If you want to add games to your tiny new gaming system, load them up on a USB drive as instructed here. Then, using the included micro USB adapter, transfer them using the USB port on the Raspberry Pi Zero labeled 'USB'.