To make MySQL usable in a network environment you simply perform a standard install. MySQL is enabled for TCP/IP networking by default, so no additional steps would be required. You will of course want to make sure that any firewall between the machine hosting MySQL and the other machines in the network allows traffic on port 3306.
If you are using VB6, you will want to install MySQL Connector/ODBC for ODBC connectivity to VB6. If you are using VB.NET, take a look at Connector/NET, a managed .NET provider written completely in C#.