As Thruston says in the comments you can use the \fill
command together with a closed path to colour a region. You can also use \draw[fill=<colour>]
and many other tikz commands accept fill=...
as an argument.
To add text to the picture you can use the \node
command, which uses the syntax
\node at (x,y)[options]{text};
Alternatively, and almost equivalently, you can use:
\draw[draw options] (x,y) node[node options]{text};
For the various options for \node
and \draw
see the tikz manual.
It's not clear which regions you want to colour, so the following code does all of them:
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\foreach \ang/\col in {0/red,1/green,2/blue,3/yellow} {
\fill[\col!20] (45+90*\ang:2.8)--(0,0)--(45+90*\ang+90:2.8)--cycle;
}
\draw[thick,->] (0,-1)--(0,1);
\draw[thick,->] (-1,0)--(1,0);
\draw (-2,-2)--(2,2);
\draw (-2,2)--(2,-2);
\node at (0,1.5)[blue]{Some nice text};
\end{tikzpicture}
\end{document}
Note that you want to colour the region first so that the colours are "underneath" the rest of your drawing. For more complicated drawings you might need the tikz backgrounds
library.
The code above gives:

\fill[red] (-2,-2) -- (0,0) -- (-2,2) -- cycle;
?