$sql = "INSERT INTO `Visitors`(`Cust_id`, `first_name`, `last_name`,
`Email_address`, `Phone_no`, `St_Addr`, `city`, `State`, `zip`, `age`,
`Ethnicity`, `Signup_Date`) VALUES (".'$firstname'.", ".'$lastname'.",
".'$email'.", ".'$telephone'.", ".'$Street_Address'.", ".'$City'.",
".'$State'.",".'$ZIP'.",".' $age'." , ".'$Ethnicity'.",".'$date'.")";
Id is on auto increment
The number of columns don't match. You don't need to specify the ID if it is autoincrement.
Also '$something' will literally insert $something. You want to use " to insert dynamic data.
$sql = "INSERT INTO Visitors
(first_name, last_name, Email_address, Phone_no, St_Addr, city, State, zip, age, Ethnicity, Signup_Date)
VALUES
('".$firstname."', '".$lastname."', '".$email."', '".$telephone."', '".$Street_Address."', '".$City."', '".$State."','".$ZIP."','". $age."' , '".$Ethnicity."','".$date."')";