Okay I am not a fan of php frameworks so I will make this one for you with MySQL:
if(empty($_POST["user"]) || empty($_POST["pass"])){
echo "Missing values";
} else {
//You would need the mysql connection variable named $db_conn
$db_conn = mysqli_connect("localhost","user","pass","db_name");
$user = $_POST["user"];
$pass = md5($_POST["pass"]);//MD5 encrypt;
$sql = "SELECT id FROM users WHERE username='$user' AND password='$pass'"
$query = mysqli_query($db_conn,$sql);
if(mysql_num_rows($query) > 1){
//Do the login thingys like cookies and redirects
} else {
echo "Check your credentials";
}
}
I think I could not made it easier and better to understand