I would like to alias \mathbb as simply \bb. How do I define this new command? I know how to alias mathsymbols such as:
\def\AND{\wedge}
But I am not so sure about math commands that take parameters.
You have a number of options. Firstly you could
\let\bb\mathbb
which will copy the definition of \mathbb into \bb. This means that if the definition of \mathbb changes, \bb will remain whatever it was at the time of definition. If \mathbb were to take an optional parameter as an argument (for whatever reason), then it's more appropriate to use
\usepackage{letltxmacro}% http://tex.stackexchange.com/q/88001/5764
\LetLtxMacro{\bb}{\mathbb}
Alternatively, you could use
\newcommand{\bb}{\mathbb}
which will insert \mathbb wherever you use \bb; more akin to an alias. This has the advantage that \bb will change with any changes to \mathbb. Also, there's no need to worry about defining \bb to take the same number of arguments as \mathbb, since TeX merely replaces \bb with \mathbb. That is,
\bb{<something>}
would be interpreted as
\mathbb{<something>}
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