Ryan Kavanagh has completed a backport of BASIC-256 0.9.6.48 for Ubuntu Lucid 10.4 and Maverick 10.10. The installation for the two most recent Ubuntu releases has been made VERY EASY.
Detailed instructions for configuring the install can be found at https://launchpad.net/+help/soyuz/ppa-sources-list.html. Basically open a terminal (Applications => Accessories => Terminal) and execute the three following commands:
sudo add-apt-repository ppa:ryanakca/basic256-backports
sudo apt-get update
sudo apt-get install basic256
The first tells Ubuntu to connect to the backports, the second updates the software catalog, and the third installs the program and it's requirements.
Once the install is complete you will find BASIC-256 at Application => Science => BASIC-256.