If you have the hardware, you can do without an AWS account (you might need to be an "expert" to interpret the instructions to run on your own hardware instead of AWS). I used my gaming rig with a 1080 GTX Ti card.
You _can_ run it on a CPU, and that can work fine for very simple models (like the Tensorflow demos with MNIST) but anything much larger and things really start to take forever. Like, you'll be waiting for months.
The AWS P2 instances recommended for the course ($0.90/hour) have half a K80, which has access to 12 GB of VRAM. The list price for that card is $5000.
The GTX 1080 Ti has almost as much VRAM as half a K80, 11GB, and can be found for around $700.