How can I get cleveref to surround references with parentheses automatically?

Referencing Section 8.2.1 of the cleveref documention,

Cross-reference formats for single cross-references are defined or redefined using the \crefformat and \Crefformat commands, which are used by the \cref and \Cref commands respectively. These take two arguments: the cross-reference type, and the formatting code: \crefformat{type}{format}

For your purposes, we can use, for example:

\crefformat{figure}{(Figure~#2#1#3)}
\Crefformat{figure}{Figure~#2#1#3}

Note that I've used crefformat for use with the \cref command (not beginning of sentence), and Crefformat for use with the Cref command (beginning of sentence).

This gives

A complete MWE follows

% arara: pdflatex
% arara: pdflatex
\documentclass{article}
\usepackage{cleveref}
\crefformat{figure}{(Figure~#2#1#3)}
\Crefformat{figure}{Figure~#2#1#3}
\begin{document}

\begin{figure}[!h]
    \rule{3mm}{2mm}
    \caption{August}
    \label{fig:foo}
\end{figure}

X exhibits Y \cref{fig:foo}.

\Cref{fig:foo} is a cross reference at the beginning of a sentence
\end{document}

I would not modify the workings of \cref and friends directly. Instead, I would create a new macro called \pcref -- short for "parenthetic \cref", I suppose -- as follows:

\newcommand\pcref[1]{(\cref{#1})}

As you can probably guess, \pcref places round parentheses around the output of \cref. No need for lots of separate \crefformat directives. This approach preserves access to the standard definition of \cref, should the need to do so arise.

For the following screenshot, I loaded the hyperref package and specified the cleveref option nameinlink, in order to make visible what is, and is not, produced by \cref.

\documentclass{article}
\usepackage[colorlinks,allcolors=blue]{hyperref} % optional
\usepackage[noabbrev,nameinlink]{cleveref}
\newcommand\pcref[1]{(\cref{#1})}
\begin{document}
\begin{figure}[t!] \caption{foo}\label{fig:foo}\end{figure}
\begin{figure}[h!] \caption{bar}\label{fig:bar}\end{figure}
\begin{table}[h!] \caption{foo}\label{tab:foo}\end{table}

\dots\ \pcref{fig:foo}, \pcref{fig:foo,fig:bar}, \pcref{tab:foo,fig:bar}, \dots

\bigskip vs.

\bigskip
\dots\ \cref{fig:foo}, \cref{fig:foo,fig:bar}, \cref{tab:foo,fig:bar}, \dots

\end{document}