1. Install the necessary dependencies
As root, type:
apt-get install build-essential
apt-get build-dep banshee
For the last one, make sure you have sources repositories enabled in your /etc/apt/sources.list file (there is a line which starts with deb-src).
2. Download the source tarball
Download the source tarball from here, under the Source releases, then change the current working directory to where you saved the archive, and uncompress it:
tar -xjf banshee-1-1.2.0.tar.bz2
Change the working directory to banshee-1-1.2.0, and proceed to the next step.
3. Compile Banshee 1.2.0
In the banshee-1-1.2.0 directory, issue the usual:
The last command as root. Banshee 1.2 should be now properly installed. Run it as banshee-1 from command line or pressing ALT+F2 and typing the name in the run dialogue that appears.
Running Banshee 1.2.0