First of all you need to create a table call it Users with UserName and Password fields.
When a user register with you, you'll insert his UserName and Password in Users table (Assume you're using a form for signing up and field's names are signUserName and signPassword):
<?
$EncryptedPassword = md5($_POST[signPassword]);
$UserName = $_POST[signUserName];
$Query = "INSERT INTO Users (UserName, Password) VALUES ('$UserName','$EncryptedPassword')";
$Result = mysql_Query($Query);
?>
and when you the user wants to login, just check his UserName and Password (Assume you're using a form for login and the field's names are loginUserName and loginPassword):
<?
$UserName = $_POST[loginUserName];
$Query = "SELECT Password FROM Users WHERE UserName = '$UserName'";
$Result = mysql_query($Query);
$EncryptedPassword = md5($loginPassword);
$row = mysql_fetch_array($Result);
$PasswordFromDB = $row[0];
if ($EncryptedPassword == $PasswordFromDB)
{
echo "You're logged in!";
}
else
{
echo "You're not authorized";
}
?>
I hope this will help you.