Defining a custom environment with per-section numbering

Question

I have an enumerate environment that I want to refer to later in my document using \ref and \label, but enumerate doesn't get numbered by section (the way, say, figure would). How can I add section numbers to enumerate?

I do not want individual, enumerated items to be numbered. Rather, I want the enumeration as a whole to be numbered.

What I am really looking for is something like this:

---

Algorithm 1.2

1. Walk to store.
2. Buy Milk
3. Walk Home

... /snip/ ...

As described in Algorithm 1.2, it's easy to buy milk.

---

I don't want to use a figure because I can't have it moving around the document. I don't want to use the theorem/definition/proof environments because of all the styling. The algorithm environments use a lot of styling too. I'm basically looking for a way to slap a title on my enumerate environment and give it a number that I can refer to.

Edit:

This is what I finally ended up with, based on Mico's post:

\usepackage{amsmath}
\newcounter{algcounter}
\newenvironment{alg}{
\bigskip\noindent
\refstepcounter{algcounter}
\textbf{Algorithm \thealgcounter}
\newline
\begin{enumerate}
  \setlength{\itemsep}{1pt}
  \setlength{\parskip}{0pt}
  \setlength{\parsep}{0pt}
}{\end{enumerate}}
\numberwithin{algcounter}{section}

Answer 1

If you're willing to load the amsmath package (you may be doing so already anyway...), you can just issue the command

\numberwithin{enumi}{section}

to have level-1 enumerations be subordinated to the section.

Addendum. From your follow-up remarks, it would appear that you're not trying to change the appearance of LaTeX's own enumerate environment but, instead, want to create a custom environment that will be numbered within sections. (I.e., each time a \section command is encountered, numbering should start over at "1"; however, the section number needs to be prefixed to the environment number.) The following MWE illustrates how this may be achieved.

\documentclass{article}
\usepackage{amsmath} % needed for its \numberwithin command
\newcounter{myalgctr}

\newenvironment{myalg}{%      define a custom environment
   \bigskip\noindent%         create a vertical offset to previous material
   \refstepcounter{myalgctr}% increment the environment's counter
   \textsc{Algorithm \themyalgctr}% or \textbf, \textit, ...
   \newline%
   }{\par\bigskip}  %          create a vertical offset to following material
\numberwithin{myalgctr}{section}

\begin{document}
\section{First section}

Some text before the first algorithm environment \ldots

\begin{myalg}
Some thoughts\ldots \label{alg:first}
\end{myalg}

\begin{myalg}
More thoughts\ldots \label{alg:second}
\end{myalg}

Some text after the second algorithm environment \ldots

\section{Second section}

\begin{myalg}
Further thoughts\ldots \label{alg:third}
\end{myalg}

\section{Third section}

As we showed in algorithms \ref{alg:first}, \ref{alg:second}, 
and \ref{alg:third}, \ldots 
\end{document}

Answer 2

EDIT:

Based on the new informations of the comments I provide a new answer.

To type an algorithm you can work the the package algorihtm. By using the command numberwithin (provided by amsmath) you can set the counter:

\documentclass[a4paper,11pt]{article}
\usepackage{algorithmicx}
\usepackage{algorithm}
\usepackage{algpseudocode}
\usepackage{amsmath}
\numberwithin{algorithm}{section}
\begin{document}
\section{foo}
\begin{algorithm}
\caption{Algorithm}\label{algo}

\begin{algorithmic}[1]
\Require $x\ge5$
\Ensure $x\le-5$
\Statex
\While{$x>-5$}
\State $x\gets x-1$
\EndWhile
\end{algorithmic}
\end{algorithm}
\ref{algo}
\end{document}

To manipulate list environments like enumerate I really recommend the package enumitem. The package provides the key ref to manipulate the format of references.

Here an example:

\documentclass{article}

\usepackage{enumitem}
\setlist[enumerate,1]{ref=\thesection.\theenumi}

\begin{document}
\section{foo}
Text
\begin{enumerate}
\item \label{enum1} foo
\item \label{enum2} bar
\end{enumerate}

\ref{enum1} and \ref{enum2}
\end{document}