Multiline equation with specific indentation style

A simple solution with \phantom command:

\begin{equation}
\begin{split}
f(x,y) & =a\\
       & =b\\
       &\phantom{=}\, +c\\
       &\phantom{=}\, +d.
\end{split}
\end{equation}

gives:

This is the better looking alignment, in my opinion. Anyway, you can adjust it with spacing commands. For example, the following code

\begin{equation}
\begin{split}
f(x,y) & =a\\
       & =b\\
       &\phantom{=}\, +c\\
       &\quad +d\\
       &\phantom{=}\; +e.
\end{split}
\end{equation}

produces:

As you can see, a little spacing is added in consecutive lines.

You can just "flip around" the use of the alignment character &:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}
\begin{equation}
  \begin{split}
    f(x,y) & =a \\
    & =b \\
    & +c \\
    & +d.
  \end{split}
\end{equation}

\begin{equation}
  \begin{split}
    f(x,y) ={}& a\\
    ={}& b \\
    & {}+c \\
    & {}+d.
  \end{split}
\end{equation}
\end{document}

The additional empty groups {} ensure the correct spacing around binary operators/relations. If you wish the alignment of the +s to be more aligned with the RHS of the equations above, you could also use:

\begin{equation}
  \begin{split}
    f(x,y) ={}& a\\
    ={}& b \\
    & \mskip-\medmuskip +c \\
    & \mskip-\medmuskip +d.
  \end{split}
\end{equation}

which removes the space around the binary operator +.