There's no need to use a regex for this (in fact it would take more work). Use PHP's built-in date/time functions instead:
strtotime: converts a string date (of practically any format) to a Unix timestamp
date: formats a timestamp into a human-readable date
$user_date; #the user-supplied date, any format
$format = 'm/d/Y'; #your desired date format, in this case MM/DD/YYYY
#convert the date to your format
$formatted_date = date($format, strtotime($user_date));
Or, you can do this with a DateTime object. Given $user_date and $format from the above:
$user_date_obj = new DateTime($user_date);
$formatted_date = $user_date_obj->format($format);
or
$formatted_date = date_format(date_create($user_date), $format);
..
All that said, to answer your question, just delimit your regex. Slashes will work, but since you're matching literal slashes inside the regex, it's easier to use something else, say, bars/pipes:
preg_match_all("|[0-9]{0,2}/[0-9]{0,2}/[0-9]{4}|", $string, $matches);
That way, you don't need to escape your slash literals.
By the way, you can also shorten this regex to:
"|(\d{0,2}/){2}\d{4}|"
\d is the same as [0-9], and you can combine the two occurrences of \d{0,2}/ into (\d{0,2}/){2}. Some might find this harder to read, though.