I'm definitely not a networking guy, but by reading the documentation for Hyper-V that comes with the image, I actually figured out how to change settings correctly for the image.
First you need two network cards for the machine. One for running its own private network, and one to give it Internet access through your physical machine.
These are the settings for the first card:
Notice the network name: AX2012.
And these are the settings for the second card:
After starting the image, you need to do some configuration of the network card running the internal network. To figure out precisely what card that is, open a command prompt and enter ipconfig to check IP addresses of the cards. It should be the card having an IP address starting with 169.
From the Control Panel you must now open Network and Sharing Center and click Change adapter settings. On the card running the internal network, right-click and choose Properties.
Select Internet Protocol Version 4 (TCP/IPv4):
Now click Properties and enter the following information:
Click Advanced to open this dialog:
And here you need to enter all these IP addresses, with subnet mask 255.255.255.0:
Save everything and reboot.
It takes quites a while for both AX and the portal to come alive, so be patient.
For the two other machines that are involved in the full demo setup, you probably need to do the same. The IP addresses to add are different though. You can see the numbers in the Hyper-V documentation that comes with the image.
Any comments to guide me and the rest of the community to an eventual better process are welcome. It is very limited what kinds of questions I'll be able to answer.