The driver needed for the virtual network interface created by VirtualBox is not included in Vista by default, but it is in Windows XP. To install the driver, I think you need only install the guest additions, or if it's not part of the guest additions, it's on the CD image that gets mounted when you install the guest additions.
This is covered in greater detail in the user manual
Originally Posted by UserManual.pdf
4.2.4 Windows Vista networking
Windows Vista no longer ships a driver for the AMD PCnet Ethernet card that
VirtualBox provides to the guest by default. As a result, after installation of Vista in
a virtual machine, there will be no networking initially. As a convenience, VirtualBox
ships with a driver for the AMD PCnet card, which comes with the Windows Guest Additions.
If you install these in a Vista guest, the driver will automatically be installed
If, for some reason, you would like to install the driver manually, you can find it
on the Guest Additions ISO. To install this driver, mount the Guest Additions ISO (as
described above, select “Install guest additions” from the “Devices” menu). Then, start
the Windows Hardware Wizard and direct it to the Guest Additions CD where a driver
for the PCnet card can be found in the directory AMD_PCnet.
Alternatively, change the Vista guest’s VM settings to use an Intel networking card
instead of the default AMD PCnet card; see chapter 3.7.5, Network settings, page 46