How do I indicate an en-dash while in math mode using LaTeX?

The simplest way is to use $S=1\mbox{--}2$. If you already have \usepackage{amsmath} in your document's preamble, however, you're better off using \text: $S=1\text{--}2$ because \text will adjust the size of the font when used in super- and subscripts: $S_{1\text{--}2}=0$.

An en dash used in math may easily be confused with a minus sign. You may want to look at other techniques for indicating a range such as ellipses (\ldots for dots on the baseline [used between commas], or \cdots for centered dots [used between centered operators such as plus signs]) or using the bracket notation. Some examples:

$S = \{1, 2, \ldots, n\}$ indicates an element in the set containing integers between 1 and $n$.
$S = [0, 1]$ indicates a real number between 0 and 1 (inclusive).

You can use \textrm which does not depend on \usepackage{amsmath}. Some examples:

$S=1\textrm{--}2$
$S_{1\textrm{--}2}=0$ % correctly changes the font size for subscript
$S_{1\textrm{2}2}=0$  % does not change the font size :(

Or maybe use \textnormal instead of \textrm. See also LaTeX: use \textnormal instead of \textrm (or \textsf) in math.

Well, you could use $1\mbox{--}2$, but I'd look at the list of math symbols in the symbol list. Hmm. I don't find one.

Use the command \leftrightline in the package MnSymbol. I don't know if it's the length needed for your purposes, but hopefully it will do the trick.