Following the documentation of the calligra package at http://ctan.org/pkg/calligra, try this minimal example:
\documentclass{article}
\usepackage{calligra}
\usepackage[T1]{fontenc}
\begin{document}
Fee, fi, fo, fum.
{\calligra Foo bar bas; quux!}
\end{document}
Note that loading the package enables the \calligra command to change the font. The package also provides the \textcalligra{} command to set runs of text in that font. Either option is more convenient than loading the font yourself.
If you want to load the font yourself however, try \fontfamily{calligra}, with the font name in lowercase. (Take a look at how the package loads the font for an example; or see Herbert’s answer for details.)
If these don't work, then perhaps the font package is not installed. It is available under both MiKTeX and TeX Live; see your distribution’s instructions for installing packages.