typesetting in the style of Turing's famous "ON COMPUTABLE NUMBERS"

This can give you a starting point:

\begin{filecontents*}{examplexyz.bib}
@article{alonzo,
title={An Unsolvable Problem of Elementary Number Theory},
author={Alonzo Church},
journal={American Journal of Mathematics},
volume={58},
number={2},
month={April},
year={1936},
pages={345-363}
}

\end{filecontents*}

\documentclass[12pt,twoside]{article}
\usepackage[T1]{fontenc}
\usepackage[paperwidth=6.27in,paperheight=9.69in,centering]{geometry}
\usepackage[style=authoryear]{biblatex}
\usepackage[symbol*,bottom]{footmisc}
\usepackage[pagestyles]{titlesec}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{array}
\usepackage{fouriernc}
\usepackage{lipsum}

\addbibresource{examplexyz.bib}

\newpagestyle{mypstyle}{
  \sethead[\thepage][\scshape\Author][{[Aug, \number\day}]{\number\year]}{\scshape\Title}{\thepage}
  \setfoot[][][]{}{}{}
}
\pagestyle{mypstyle}

\DefineFNsymbols*{mystyle}{{$\dagger$}{$\ddagger$}\S\P\|%
*{**}{$\dagger\dagger$}{$\ddagger\ddagger$}}

\setfnsymbol{mystyle}

\newcommand\periodafter[1]{#1.}
\titleformat{\section}
  {\normalfont\filcenter}{\thesection.}{0.5em}{\itshape\periodafter}

\title{On computable numbers, with an application to the  entscheidungsproblem}
\author{A. M. Turing}

\makeatletter
\def\Title{On computable numbers.}
\let\Author\@author
\renewcommand\footnoterule{%
  \kern-3\p@
  \hrule
  \kern2.6\p@}
\def\@maketitle{%
  \newpage
  \begin{center}%
  \let \footnote \thanks
    {\MakeUppercase{\@title}\par}%
    \vskip 1.7em%
    {\lineskip .5em%
      \begin{tabular}[t]{c}%
        \textit{By}~\@author
      \end{tabular}\par}%
    \vskip 0.8em%
    {\footnotesize\@date}%
  \end{center}%
  \par
  \vskip 0.5em%
}
\makeatother

\begin{document}
\maketitle

\section{Computing machines}
\lipsum[4]\lipsum[4]
Test text\footfullcite{alonzo}
\lipsum[4]
The machine is to have the four $m$-configurations, ``$\mathfrak b$'', ``$\mathfrak c$'', ``$\mathfrak k$'', ``$\mathfrak e$'' and is capable of printing ``$0$'' and ``$1$''. The process of printing this $1$ will be called marking $\beta$ (or $S$) with $a$. 
\[ 
\lambda w \biggl[ \{W_\gamma\} \bigl(\bigl\{\{Q\}(W_\gamma)\bigr\} (w)\bigr)\biggr] 
\]
\lipsum*[2]
\begin{center}
\renewcommand\arraystretch{1.5}
\begin{tabular}{>{$}c<{$}>{None}c*{2}{>{$}c<{$}}}
\multicolumn{2}{c}{\itshape Configuration} & 
  \multicolumn{2}{c}{\itshape Behaviour} \\
\multicolumn{1}{c}{\itshape $m$-config.} & 
  \multicolumn{1}{c}{\itshape symbols} & 
  \multicolumn{1}{c}{\itshape operations} & 
  \multicolumn{1}{c}{\itshape final $m$-config.} \\
\mathfrak b & & P0,R & \mathfrak c \\
\mathfrak c & & R & \mathfrak e \\
\mathfrak e & & P1,R & \mathfrak k \\
\mathfrak k & & R & \mathfrak b
\end{tabular}
\end{center}
\lipsum[2-4]

\end{document}

An image of the resulting document:

Comments

• The geometry package was used to produce the paper dimensions used in the article: 6.27inx9.69in; the centering option was used to produce equal values for the margins in twoside.

• The titlesec package was used to customise the format for section titles; a similar job can be done for other sectional units.

• The pagestyles option for titlesec was used to produce a pagestyle having headers as in the original documents; this could have also been done using fancyhdr.

• biblatex and its \footfullcite commands were used to produce the full citations as footnotes.

• I used the footmisc package with the symbol option; this, together with the use of \DefineFNsymbols allows you to define the set of symbols that yu want to be applied to footnote markers.

• I redefined \footnoterule so that the rule separating text from footnotes spans the whole text width.

• I also redefined \@maketitle to emulate the style of the title information. Another option here, would be to use the titling package.

• I defined some auxiliary commands \Title and \Author to have the author and (part of the) title in the headers.

• In a comment to the question, sgmoye identified the font as pertaining to the Century family of typefaces. According to the LaTeX Font Catalogue, the fouriernc package provides support for New Century Schoolbook for LaTeX. The following uses this package; as sgmoye warns, "the matching to the original is not exact, but captures the flavour of the original".

• After a suggestion by barbara beeton, I added some elements from the original document (a bit of maths and one of the tables), to show the blend between text and math fonts. barbara beeton kindly provided the math expressions.

I don't have such a template. I see couple things that should be done when writing the article, and IMHO it is too much to be just a comment.

1. Notice that § (coded as \S) stands for "section" and §§ (coded as \S\S) stands for "sections", as was usual back then.

2. The quotation marks are badly-spaced, and they should be written as `{}` and '{}' or with the appropriate ligatures disabled (this is possible via fontspec in XeLaTeX and LuaLaTeX).

3. To simulate the effect of non-uniform letters, you can use \usepackage[stretch=70]{microtype}, which will allow the font to stretch and shrink from line to line, creating such an effect.