\documentclass[12pt]{amsart}
\usepackage{fixltx2e}%% the official fixes for LaTeX2e
\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc}
\usepackage[scaled=0.92]{helvet}
\usepackage{mathptmx}
\usepackage{courier}
\makeatletter
\def\verbatim@font{\small\normalfont\ttfamily}
\makeatother
\theoremstyle{plain}    
\newtheorem{thm}{Theorem}[section]
\theoremstyle{plain}
\begin{document}
class ams-article 

now I start a theorem

\begin{thm}
my theorem
\begin{enumerate}
\item enum 1
\item enum 2
\item enum3
\end{enumerate}
next theorem line
\end{thm}
The steps to get this:

\begin{enumerate}
\item choose layout theorem
\item write the whole stuff inclusive the enumerate one without changing
anything.
\item bla blah blah blubber
\item bla blah blah blubber
\end{enumerate}
That's all. now the same for proof.

\begin{proof}
My Proof

choose layout theorem
\begin{enumerate}
\item choose layout theorem
\item write the whole stuff inclusive the enumerate one without changing
anything.
\item bla blah blah blubber
\item bla blah blah blubber
\end{enumerate}
\end{proof}
The end
\end{document}