For the sake of completeness...
Q: Do I need to create a directory where to store these pictures?
Q: What should be the location of this directory?
It is not necessary to put the figures (or other files required for the typesetting of the document, as tex files, bib files, etc...) into specific directories. This means that you can organize your files in a way that suits to you, and latex and friends can be persuaded to adapt to your structure. It is just a matter of specifiyng the path unambiguously. Defining a relative path as Umar Kalim does in his answer is a good practice, minimizing both keystrokes and errors.
Q: What kind of file extensions do I need to have for these files?
If you want to include figures, you will probably want to use the includegraphics command from the graphicx package. If you specify the filename without extension, as in \includegraphics{path/to/file}, the eps extension will be added when compiling with latex, and the pdf extension will be added when compiling with pdflatex (for this to work the two versions of the file should be present in the same directory).
The file types supported natively are:
latex: can include EPS files with graphicx package (some dvi viewers may fail to show the image though)
pdflatex: according to the manual page,
In PDF mode, pdfTeX can natively handle the PDF, JPG, JBIG2, and PNG graphics formats.
As stated in Umar's answer, with the epstopdf package it is possible to include eps graphics into pdf files (the package automatically converts the file to pdf format, so the tool epstopdf needs to be present in your system)
If your file is not in any of these formats, it has to be converted to one of the above mentioned. Automatic conversions (i.e., performed by (pdf)latex at compilation time) can be forced using the \DeclareGraphicsRule command: take a look at Using macros in \DeclareGraphicsRule statement using shell command, Add tif image to LaTeX and related questions.
.epsfiles in the same folder than yourtexfile. This answer, however can be elaborated if you want the figures in a different folder, or if your "main document" is indeed a bunch oftexfiles in different folders. – JLDiaz Feb 14 at 17:33