First of all, make sure that you're familiar with the php/MySQL design
http://www.w3schools.com/php/php_mysql_intro.asp
This process should be simple: take one form:
<form method='post' action='pagename.php'>
Email Address <input type='text' name='email' />
Confirm Email <input type='text' name='confirmemail' />
<input type='submit' value='Sign up!' />
</form>
Once this form is submitted, the code to handle it will be
if(isset($_POST['submit']) && $_POST['email']==$_POST['confirmemail'])
{
mysql_query("INSERT INTO table VALUES value1, value2");
}
which will add the email address' into the database after checking that the 2 emails address' match (you may also need to put in some of your own validation ie checking that the email address is valid. stripslashes() etc.
Then on your page where you have a form to make your news letter?
<form method='post' action='page2.php'>
<textarea cols='50' rows='25'></textarea>
<input type='submit' value='Send Letter' />
</form>
This form allows you to write your letter and send it.
The page it directs to should then have the appropriate code to retrieve email address' from the database and send the letter.
if(isset($_POST['submit'])
{
$query = mysql_query("SELECT emailaddress FROM table"); <--- the table you saved the email address' to
while($row = mysql_fetch_array($query)) <--- while there are email address' to be sent to
{
mail($row['email'], $subject, $newsletter); <--- send the email.
}
}
If you're unsure about the email function then check here
http://www.w3schools.com/php/php_mail.asp