I found the following solution for my environment:
- first adapter with internal network to access the other VM-
- second adapter with NAT to access the internet.
Those settings can be done by the GUI Oracle VM VirtualBox Manager. Initially I had the same problem as Jonas, I missed DHCP. Finally I found this article (archived copy, this articleoriginal link is dead) and I used:
VBoxManage dhcpserver add --netname intnet --ip 10.13.13.100 --netmask 255.255.255.0 --lowerip 10.13.13.101 --upperip 10.13.13.254 --enable
from the command line. Afterwards it worked fine.
I dare say that the manual is a poor resource, as most of the configuration of VirtualBox on a Windows host can be done by the GUI and it is a severe inconvenience that one can't configure DHCP with the GUI.
My environment: I'm running portable VirtualBox 4.1.2r73507 on Windows 7 64 bit. Currently host-only and bridged mode not working, because host-only adapter is missing. I have a problem similar to that described in a german question on Virtual Box forum, I have no host only adapter.