You can install this package with dpkg -i if dependencies are already installed, or use a tool such as gdebi to resolve dependencies for you. So far this package has only been install tested on Ubuntu Lucid, but please let us know how you get on.
Liquidsoap 1.0.0 or higher is required, as it was for Airtime 2.0.x packages. The Liquidsoap package provided in Ubuntu Precise should be suitable, but for other distros please use the packages provided from http://apt.sourcefabric.org/
Soon we will be providing an enhanced Liquidsoap package that enables smoother stream transitions, but plain Liquidsoap 1.0.0 should function as always.
Just a quick note, for users with newer versions of Ubuntu (where gdebi is not installed) simply double clicking the Debian package in the file manager will allow you to install it using Ubuntu Software Center.