Free BASIC Tutorials
QBasic wikibook 
This is the wikibook entry for QBasic. It is really more of a short QBasic tutorial than a book.
QBasic - Step By Step
QBasic tutorial covering fundamental aspects of the language, input and output, control structures, modules / sub procedures, looping, functions, arrays, array-type problems, records, and data files.
Using Liberty BASIC 2
Liberty BASIC tutorial.
Qbasic Tutorial
About five chapters...looks like a good tutorial.
Programming in (Q)BASIC
Introductory level tutorial.
QBASIC TUTORIAL
A pretty comprehensive one-page tutorial.
This is how to use BASIC
A one-page tutorial with brief coverage of keywords, variables, operators, functions, and conditionals
Tutorials for Liberty BASIC 1.4
A list of tutorials that are downloadable in zip format.
Qbasic Tutorial
QBasic is a very simple language to pick up, and yet it can accomplish a great deal.
QBasic
QBasic tutorial.