Let's demonstrate how you can achieve this with biblatex, which comes with in-built support for APA style; technically, we'll actually be using biber, which is a 'backend bibliography processor for biblatex'
We will have the following files in the same directory
myfile.tex
\documentclass{article}
\usepackage[american]{babel}
\usepackage{csquotes}
\usepackage[style=apa]{biblatex}
\DeclareLanguageMapping{american}{american-apa}
\addbibresource{mybib.bib}
\begin{document}
\begin{itemize}
\item \verb!\cite! \cite{Ab_Steg}
\item \verb!\textcite! \textcite{Ab_Steg}
\item \verb!\parencite! \parencite{Ab_Steg}
\end{itemize}
\printbibliography
\end{document}
mybib.bib
@BOOK{Ab_Steg,
author = "M. Abramowitz and I. A. Stegun",
title = {Handbook of mathematical functions},
publisher = "Dover publications",
year = "1965",
language="English" }
To compile this, you run
pdflatex myfile
biber myfile
pdflatex myfile
pdflatex myfile
note that each command doesn't have an extension- if you wanted to, you could use the extensions
pdflatex myfile.tex
biber myfile.bcf
pdflatex myfile.tex
pdflatex myfile.tex
This gives the following output

To facilitate this process we can use the excellent arara automation tool to help- we can change myfile.tex to include the following lines
% arara: pdflatex
% arara: biber
% arara: pdflatex
% arara: pdflatex
\documentclass{article}
\usepackage[american]{babel}
\usepackage{csquotes}
\usepackage[style=apa]{biblatex}
\DeclareLanguageMapping{american}{american-apa}
\addbibresource{mybib.bib}
\begin{document}
\begin{itemize}
\item \verb!\cite! \cite{Ab_Steg}
\item \verb!\textcite! \textcite{Ab_Steg}
\item \verb!\parencite! \parencite{Ab_Steg}
\end{itemize}
\printbibliography
\end{document}
which gives
__ _ _ __ __ _ _ __ __ _
/ _` | '__/ _` | '__/ _` |
| (_| | | | (_| | | | (_| |
\__,_|_| \__,_|_| \__,_|
Running PDFLaTeX... SUCCESS
Running Biber... SUCCESS
Running PDFLaTeX... SUCCESS
Running PDFLaTeX... SUCCESS
.bib. The quickest way to try out is JabRef. It's fairly easy to populate a database with it and you don't need any TeX knowledge to obtain a.bibfile. If you alredy have a.bibfile then you can look at the questions tagged with apa-style and bibtex for possible use cases. – percusse Mar 10 at 10:57