It is a common misconception that VPN connections require a dial-up connection. They require only IP connectivity between the VPN client and VPN server. Some clients (such as home computers) use dial-up connections to the Internet to establish IP transport. This is a preliminary step in preparation for creating a tunnel and is not part of the tunnel protocol itself.
That attitude to the safety and privacy of personal data creates an enormous online security risk. Public Wi-Fi networks, which are ubiquitous and convenient, are unfortunately also highly convenient for attackers looking to compromise your personal information. How do you know, for example, that "starbucks_wifi_real" is actually the Wi-Fi network for the coffee shop? Anyone could have created that network, and they may have done so in order to lure victims into disclosing personal information over it. In fact, a popular security researcher prank is to create a network with the same name as a free, popular service and see how many devices will automatically connect because it appears safe.