Latex: how to break a line inside $$

A couple of people have suggested eqnarray which will work, but a better approach is the align environment in the amsmath package.

\begin{align*}
something \\
something else
\end{align*}

If you want the two parts aligned in some way, use an & as described in the amsmath documentation.

Instead of using the TeX-style $$ commands, consider using the align* or gather* environments. Inside those, you can use the line break command \\.

(You will need to load the amsmath package to use those; but if you're doing any math at all, you should be loading that package regardless.)

The way to get line breaks in display math, while using only standard LaTeX, is to use \begin{array}...\end{array} within the display math environment $$...$$. (Yes, I know that $$ is deprecated but I still like it.) There are many alternatives in different extensions, including AMSLaTeX's align and align* environments. My personal favorite is Didier Rémy's mathpartir package, which gives a display-math environment that is more like paragraph mode, plus a set of tools for typesetting logical inference rules and proof trees.

11 years later...

An example of breaking text in multiple lines is having a cell with multiple lines in an array. Instead of using a new array row, you can break the text in lines within a cell. The advantage of doing this is interline space is not dependent on the whole row height (if some cell in the row has a large height, this won't influence the text interline space):

To do this, just enclose the cell content within curly braces and use \\ as a linebreak.

Content of the highlighted cell:

{ T_f (u) \text { is the transformed function and }
  \\
  K (t,u) \text { is the kernel used. }}

Whole code:

$\begin {array} {lll}
\text {Transform: } T_f (u) 
    & = \int \limits_{t_1}^{t^2} K (t,u) f(t) dt \;\; \textrm {where:}
        & {
            T_f (u) \text { is the transformed function and }
            \\
            K (t,u) \text { is the kernel used. }
          }
          \\
\text {Inverse transform: } f(u) 
    & = \int \limits_{u_1}^{u^2} K^{-1} (t,u) T_f(u) du
\end {array}$

Try something like this:

    \documentclass[varwidth,margin=3mm]{standalone}
    \usepackage{amsmath}
    \begin{document}
        \begin{math}
                \alpha(e1)=c1,\ \alpha(e2)=c3\\
                \alpha(e3)=c5,\ \alpha(e4)=c2\\
                \alpha(e5)=c4,\ \alpha(e1)=c1\\
        \end{math}
    \end{document}

The varwidth parameter is the key.
With it you can properly utilize \linebreak, \newline, \\, etc.
I used \begin{math} / \end{math}, but you should be able to use the old $ / $$ notation too.

You could use an eqnarray* instead.