That's easy.

You have three options, one of which you won't enjoy hearing:
1. Download a DOS emulator like DOSBox or DOSEMU.
2. Download an emulator Bochs or VM software like VMware, and set it up to run DOS (you need a copy of some form of DOS).
3. Download FreeBasic.

Yes, I wrote that last one. IMHO, the communities really shouldn't be so torn. After all, if it wasn't for QBasic, FreeBasic wouldn't exist. You might consider compiling it from source if you have all of the necessary components (SDL, libpng and other graphics libraries are fairly crucial for programs that use screen modes other than 0).

On the other hand, DOSBox can be easily installed via a package manager if you have Internet access. That's an equally good idea (assuming you don't feel that it's a better idea). From there, you can just download DOSBox via Ubuntu's own Universe repository. Then you could download QBasic from the Internet (or your computer, depending on your experience with Samba/CIFS) and use DOSBox that way. I'm not too familiar with DOSEMU because DOSBox has worked for me every time on both Windows and Linux.

The other option is using something along the lines of an emulator like Bochs, so that you could install some form of DOS that will run QBasic (I believe FreeDOS works, and it's free).

If you don't have Internet access on your Ubuntu machine to download anything with your package manager, then you would need to download it and all of its dependencies that you don't have (and the dependencies of the dependencies) from packages.ubuntu.com. DOSBox and DOSEMU are in the "Other OS's and file systems" subsection of your Ubuntu version (e.g. `hardy').

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Waiting patiently for XHTML 2.0, CSS 3.0, the ratification of C++0x, and the day that I can code without logic troubles.