> How can I put a box around several paragraphs?
>
> I tried \parbox and \begin{minpage} according to the books, but why
> not box lines show up? What should I do?

They don't give box lines. A "box" in that context is an object that holds its contents together in one piece; makes it behave like a single character, according to the LaTeX manual.

What you seek is a "frame". Thus \fbox{} or \framebox{}. To frame a paragraph, you need to put \fbox{parbox{}{ }}. You probably also want a larger setting of \fboxsep.

> \begin{center}\begin{figure}[!ht]\begin{center}
> \parbox{5in}{\begin{flushleft}
> Given query instance $x_q$,  \newline
>  first locate nearest training example $x_n$, \newline
>  then estimate $\hat{f}(x_q) \equiv f(x_n)$.
> \caption{Nearest Neighbor Algorithm}
> \end{flushleft}}\end{center}
> \end{figure}\end{center}

Get rid of the outermost center environment; it introduces space outside of the figure.

You may also want to look up the simple sty file boxedminipage.sty.

Finally, for this algorithmic example, which is not a natural paragraph, I think it would work better as a tabular, which can also provide the frame:

\begin{figure}[!ht]
\centering % no extra space that {center} would give

\begin{tabular}{|l|}\hline
 Given query instance $x_q$,  \\
 first locate nearest training example $x_n$, \\
 then estimate $\hat{f}(x_q) \equiv f(x_n)$. \\ \hline
\end{tabular}

\caption{Nearest Neighbor Algorithm}

\end{figure}

Donald Arseneau