How to split cell text into multiline in table?

Package tabularx is your friend:

\documentclass[twocolumn]{paper}
\usepackage{tabularx}
    \newcolumntype{L}{>{\raggedright\arraybackslash}X}

\begin{document}
    \begin{table}
    \centering
\begin{tabularx}{\linewidth}{|L|c|L|} 
    \hline
\textbf{Col1} & \textbf{Col2} & \textbf{Col3} \\ 
    \hline
This is a very long line of text & Short text & Another long line of text \\ 
    \hline
$\pi$ & 1 in 5& Common in math\\
    \hline
\end{tabularx}
    \end{table}
\end{document}

If you want to control line breaks in cells, you can use the \makecell command from the homonymous package. In addition, it has tools to add some vertical padding to cells:

\documentclass{paper}

\usepackage{array, makecell} %

\begin{document}

\begin{table}[thb]
\centering\renewcommand\cellalign{lc}
\setcellgapes{3pt}\makegapedcells
\begin{tabular}{|l|c|l|} \hline
\textbf{Col1} & \textbf{Col2} & \textbf{Col3} \\ \hline
\makecell{This is a \\very long line \\of text} & Short text &\makecell{ Another long \\line of text} \\ \hline
$\pi$ & 1 in 5& Common in math\\
\hline\end{tabular}
\end{table}

\end{document} 

Your wrong column alignment results from missing column delimiters (&) in your source code and can be fixed easily. This also fixes the broken vertical lines.

\begin{table}[thb]
    \centering
    \begin{tabular}{|l|c|l|}
        \hline
        \textbf{Col1}  & \textbf{Col2} & \textbf{Col3}  \\ \hline
        This is a      &               &    \\ % <===== note the empty cells in this line
        very long line &  Short text   & Another long   \\
        of text        &               &  line of text\\ \hline % <===== and in this
        $\pi$          &    1 in 5     & Common in math \\ \hline
    \end{tabular}
\end{table}

A less manual way would be to use the p column type, but you have to specify the column width and LaTeX will do the linebreaks for you, but your last cell will probably also break:

\begin{table}[thb]
    \centering
    \begin{tabular}{|p{1.8cm}|c|p{2cm}|}
        \hline
        \textbf{Col1}                                                                & \textbf{Col2} & \textbf{Col3}                                                         \\ \hline
        This is a very long line of text &  Short text   & Another long line of text \\ \hline
        $\pi$                                                                        &    1 in 5     & Common in math                                                        \\ \hline
    \end{tabular}
\end{table}

Or you can use the multirow package. Load \usepackage{multirow} in your preamble {anywhere between \documentclass{paper} and \begin{document}, and then you can do:

\begin{table}[thb]
\centering
\begin{tabular}{|l|c|l|}
    \hline
    \textbf{Col1}                                                     & \textbf{Col2} & \textbf{Col3}                                            \\ \hline
    \multirow{3}{*}{\parbox{1.8cm}{This is a very long line of text}} &               & \multirow{3}{*}{\parbox{2cm}{Another long line of text}} \\
                                                                      &  Short text   &  \\
                                                                      &               &  \\ \hline
    $\pi$                                                             &    1 in 5     & Common in math                                           \\ \hline
\end{tabular}
\end{table}

Note that this aligns the columns vertically centered. The \parbox{length} defines when your text should be broken.