To make a VoIP call the only additional piece of equipment that a typical setup will need is an Analog Telephone Adaptor (or ATA), which is usually supplied by the VoIP service provider when you sign up for service.
This allows you to make phone calls as normal, using your own standard phone. The ATA does the clever conversion of your analog voice to a digital signal that the Internet can understand. It then sends that signal on to your Broadband modem, which passes it over the Internet.
A typical residential VoIP solution looks like this:

Why is the computer in the picture - you still want your high speed Internet, right? You can surf the web while your daughter talks to her friends on the phone.
If you have more than one phone in your home the recommended connection is to use cordless telephones. The base station of the cordless telephone plugs directly into the VoIP ATA. The additional handsets can then be placed anywhere in your home, distributing the VoIP phone service to your required locations.
For homes with more than one computer simply connect a router to the ATA instead of the PC in the diagram above. Your computers then connect to the router. Note that many other connectivity options exist for this type of setup.