They definitely make programs that do this already. They use the voice modems to accomplish this. Microsoft probably has existing programs that do similar things built into the operating system. For instance there is a dialer as a standalone product inside of windows. Windows also has standard connection objects that let you set up a connction with a dialer to an ISP. VB should be able to use some of these objects.
The IBM Aptivas came with software to do this. Look for some programs that can also set up an answering machine on your computer or use Voicemail on your computer. There may be this type of software with some modems, and with some sound cards also. Some of these programs were basicall Phone oriented and some were Network Voice Over IP (VOIP) oriented. Using an address book you may be able to look up the phone numbers.
If they have these programs to work on Windows CE which can run on a PDA and turn a PDA into a phone, then most likely you can find a free download on the internet. You may look at some site that does .NET programming. They may have some DLL's or code written that already designed to do what you want. VB can probably take other programs and embedding them into a user interface.
If you do not like my post feel free to point out your opinion or my errors.