<p>Well, it seems simple enough, but I can't find a way to add a caption to an equation.
The caption is needed to explain the variables used in the equation, so some kind of table-like structure to keep it all aligned and pretty would be great.</p>

You may want to look at
http://tug.ctan.org/tex-archive/macros/latex/contrib/float/
which allows you to define new floats using
```
\newfloat
```
I say this because captions are usually applied to floats.
Straight ahead equations (those written with
```
$ ... $
```
,
```
$$ ... $$
```
,
```
begin{equation}...
```
) are in-line objects that do not support
```
\caption
```
.
This can be done using the following
snippet
just before
```
\begin{document}
```
```
```
\usepackage{float}
\usepackage{aliascnt}
\newaliascnt{eqfloat}{equation}
\newfloat{eqfloat}{h}{eqflts}
\floatname{eqfloat}{Equation}

\newcommand*{\ORGeqfloat}{}
\let\ORGeqfloat\eqfloat
\def\eqfloat{%
  \let\ORIGINALcaption\caption
  \def\caption{%
    \addtocounter{equation}{-1}%
    \ORIGINALcaption
  }%
  \ORGeqfloat
}
```
```
and when adding an equation use something like
```
```
\begin{eqfloat}
\begin{equation}
f( x ) = ax + b
\label{eq:linear}
\end{equation}
\caption{Caption goes here}
\end{eqfloat}
```
```