As the article title says, how do you network office branches (3)? What are the requirements to network them? And what are the best hardware and software selection?

This is a very open-ended question... There are numerous ways to connect three offices together.

Where are these offices located?
Do they have access to the Internet?
Are they within range to run a private cable between them?
Is there a telecom provider to connect into their cloud?

How much money are you willing to spend on this project?
What are the bandwidth requirements?
What are the security requirements?

The list of questions continue...more detaled information is needed to provide a good recommendation.

You can network three offices..by running cables between the offices, to wireless, to VPN connections, etc...

I assume these branches are geographically separated (in different buildings/towns/states/whatever). In such a case, you will need what is called a "Virtual Private Network", or VPN for short. There are a lot of devices and software that will let you set up such a network, allowing your offices to connect as though they were all local. There is open source software such as OpenVPN that is widely used, as well as many "appliance" systems that provide such capabilities. Which sort of VPN you use depends a lot on how sophisticated your IT people (assuming you have any) are. If you are still clueless, check with your internet service provider(s). They may have VPN services you can utilize, for a price.

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