You can do this with natbib and the bibentry package:
\documentclass{article}
\usepackage{filecontents} % only needed to include sample bib file
% This is the sample bib file
\begin{filecontents}{test.bib}
@article{glashow,
Journal = {Nucl.~Phys.},
Author = {Glashow, Sheldon},
Pages = {579--588},
Title = {Partial Symmetries of Weak Interactions},
Volume = {22},
Year = {1961}}
\end{filecontents}
\usepackage{natbib,bibentry}
\bibliographystyle{apalike}
\begin{document}
\nobibliography{test.bib}
This is a complete citation: \bibentry{glashow}
\end{document}
You can also do it easily with biblatex:
\documentclass{article}
\usepackage{filecontents} % only needed to include a sample bib file
% This is the sample bib file
\begin{filecontents}{test.bib}
@article{glashow,
Author = {Glashow, Sheldon},
Journal = {Nucl.~Phys.},
Pages = {579--588},
Title = {Partial Symmetries of Weak Interactions},
Volume = {22},
Year = 1961}
\end{filecontents}
\usepackage[style=authoryear]{biblatex}
\bibliography{test.bib}
\begin{document}
This is a complete citation: \fullcite{glashow}
\end{document}
If you are just beginning with bibliographies I would go with the biblatex solution, since it provides a much easier interface for modifying the formatting. (Although there are many existing .bst files available for natbib.)