Create a file called emails.php
Open it in notepad or whatever text editor you like.
Copy/Paste
<?php
$con = mysql_connect("host, probably localhost", "mysql username", "mysql password");
mysql_select_db("database name");
$sql = 'SELECT user_email FROM prefix_users LIMIT 0, 300 ';
$result = mysql_query($sql);
if ( ! $result )
{ echo mysql_error(); }
else{
while ($row = mysql_fetch_assoc($result)) {
echo $row['user_email'].',';
}
}
?>
Edit the hostname, database name, database username, database password at the top with your own mysql login info. If you don't know it, look in wp-config.php and it's at the top.
Save the file. Upload it to your server somewhere. Then browse to the file in your web browser. For example, if you upload it to the root of your website's directory, where the primary index file is, you can just go to domain.com/emails.php
This show you all the email addresses up to 300, separated by commas.