PS Vita: How do I connect to Wi-Fi without Wireless or 3G?

For any laptop, you could use a usb to ethernet adapter. But a PS Vita/tablet/phone will not normally be able to use such a device as the usb port hardware and/or OS kernel driver will not support it.

Easiest solution, if by "classic telephone cable connection" you meant an ethernet port: buy a cheap wireless access point (WAP), configure your PS Vita to connect to it using PSK2 and a strong password, and bring it along to plug into their ethernet.

If all they have is an actual analog phone port then things get complicated to the point where you should just forget about it. Connection would require a PC (Laptop would do ok) with an analog modem, wifi in WAP or ad-hoc mode, and routing/nat/masquerading/internet connection sharing.