I'm not sure what you mean by "more in-depth", but here's a quick overview...
In your mysql table 'companies', in a field called 'industry', you store industry group values in a field.
a = Accounting
b = Banking
c = Computers
d = Defence
In your php, you need to query the mysql, and extract those values, something like this;
$query = "SELECT * FROM companies WHERE record = '$therecord'";
$result = mysql_query($query);
Then you need to get your values like this;
$row = mysql_fetch_array($result); //assuming $therecord is a unique value (I use the autoincrement value)
Now you need to read the value and then set the radio buttons as 'checked' like this;
$type = $row[industry];
$checked[$type] = "checked";
FInally, your html looks like this;
<input type='radio' name='industry' value='a' $checked['a']>Accounting<br/>
<input type='radio' name='industry' value='b' $checked['b']>Bankng<br/>
<input type='radio' name='industry' value='c' $checked['c']>Computers<br/>
<input type='radio' name='industry' value='d' $checked['d']>Defence<br/>
Using the array $checked makes the coding exercise a little easier.
When this is submitted from the browser, the receiving script simply updates (or inserts) the value a, b, c, or d in the database.
I hope that helps.