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I'm aware of fonts such as cmr10, cmex10 and cmsy10. Right now I would like to know how to use TeX to produce symbols in the character tables such as http://www.math.union.edu/~dpvc/jsmath/symbols/cmex10.html

Is there a dictionary somewhere on the internet containing how to TeX every symbol in character tables given the font? (i.e. Given 'x41' and the font cmr10 I want to obtain 'A', given 'x00' and cmr10 I want to obtain 'textGamma').

P.S. This question is motivated by my attempts to extract text from .tex files. I end up deciding to first convert .tex files to DVI files and then use dviasm to extract the text because it bypasses the need to essentially build another TeX engine.

LaTeX Font Encodings contains font tables for every legacy LaTeX encoding in common use. The modern toolchain with fontspec simply uses the Unicode encoding (under the alias TU).

If you want to be able to copy-and-paste, or otherwise automatically convert, text from a PDF document compiled from LaTeX source, your best bet is to use unicode-math. Then, all your glyphs are already encoded in Unicode.

A font using a non-standard encoding (such as U) should come with documentation. For example, the masfonts manual comes with tables of all its fonts in an appendix.

An adjunct to the "Comprehensive LaTeX symbols list" is the "rawtables" pdf file that contains font tables for all the fonts covered by that list, arranged in alphabetical order. The font table arrangement shows the location in the font presented to TeX; it does not identify the glyphs by Unicode ID.

The collection is on CTAN: http://mirrors.ctan.org/info/symbols/comprehensive
and the pdf listing comes in either lettersize or a4.

Despite the "LaTeX" in the title, these fonts can be used also with plain TeX.

While the user specifies TeX (for Plain TeX, see SUPPLEMENT), these tables are most easily obtainable via LaTeX, in the format described by the OP at http://www.math.union.edu/~dpvc/jsmath/symbols/cmex10.html

documentclass{article}

usepackage{fonttable}

begin{document}

fonttable{cmex10}

end{document}

The same font table may be alternately obtained via xfonttable{OMX}{cmex}{m}{n}.

To answer the OP's specific question about the letter A in cmr10,

documentclass{article}

usepackage{fonttable}

begin{document}

fonttable{cmr10}

end{document}

Just remember though, that for a given encoding scheme, one knows where to find various glyphs, even without printing the font table, especially for standard glyphs such as those available in ASCII.

SUPPLEMENT

For the Plain TeX alternative (fontchart.tex, found at https://ctan.org/pkg/fontchart?lang=en), here is the result for cmr10: