Brightbox provide a local dns cache that can be used to do recursive lookups. Each Brightbox comes preconfigured to use these. From /etc/resolv.conf:
nameserver 77.240.8.253 nameserver 77.240.8.193
All Brightboxes have a default DNS setup of the form username-boxnumber.vm.brightbox.net, for example: johnl-010.vm.brightbox.net.
A wildcard record is setup by default too, which allows you to test multiple apps on your Brightbox without needing to point a new domain at it:
john@dogen:~$ host test.johnl-010.vm.brightbox.net test.johnl-010.vm.brightbox.net A 77.240.8.10 john@dogen:~$ host myapp.johnl-010.vm.brightbox.net myapp.johnl-010.vm.brightbox.net A 77.240.8.10 john@dogen:~$ host ruby-soho.johnl-010.vm.brightbox.net ruby-soho.johnl-010.vm.brightbox.net A 77.240.8.10
To point a domain at your Brightbox, just create an "A record" that resolves to the public IP of your Brightbox. Brightbox do not provide DNS services so you'll need to use a 3rd party registrar to do this.
You can get the IP address of your Brightbox using the host tool which is available on most operating systems (it's installed on every Brightbox too).
john@dogen:~$ host johnl-010.vm.brightbox.net johnl-010.vm.brightbox.net A 77.240.8.10
You still need to configure your web server to accept requests for your new domains. If you're using the Brightbox gem you can specify these in the Capistrano recipe, otherwise you can just configure Apache manually.