How do I get different colors for math and for text?

A quick way is using \everymath, \everydisplay and the everysel package:

\documentclass{article}
\usepackage{amsmath}
\usepackage{color}
\usepackage{everysel}
\EverySelectfont{\color{red}}
\everymath{\color{black}}
\everydisplay{\color{black}}
\begin{document}
text $x=0$
\[ \text{Text in math, }y= 1 \]
\end{document}

However, with more complicated amsmath environments such as align there could could be problems with \everydisplay, see: Modifying \everydisplay causes the align environment to stop working. If you would like to go this way, perhaps omit \everydisplay as align uses inline math internally, and redefine basic displayed math otherwise for using the desired color.

If you can use xelatex or lualatex to compile the document, a combination of fontspec and unicode-math can help:

\documentclass{article}
\usepackage{fontspec}
\setmainfont[Color=FF0000]{Latin Modern Roman}
\setsansfont[Color=FF0000]{Latin Modern Sans}
\setmonofont[Color=FF0000]{Latin Modern Mono}

\usepackage{lipsum}
\usepackage{amsmath}
\usepackage{unicode-math}
\setmathfont[Color=000000]{lmmath-regular.otf}

\begin{document}
A bunch of text, then an equation.
\begin{equation}
  f(x) = \sin (x) \text{ and } g(x) = e^x\cos(x)
\end{equation}
Some \textsf{inline} math \( a = b \), and then an \texttt{align}
\begin{align}
 N^2 &= -\frac{g}{\rho_0} \frac{\partial \rho}{\partial z} \\
   N &= \sqrt{-\frac{g}{\rho_0} \frac{\partial \rho}{\partial z}}
\end{align}
\end{document}