How to Create a Search Feature with PHP and MySQL

<?php
  if(isset($_POST['submit'])){
  if(isset($_GET['go'])){
  if(preg_match("/^[  a-zA-Z]+/", $_POST['name'])){
  $name=$_POST['name'];
  //connect  to the database
  $db=mysql_connect  ("servername", "username",  "password") or die ('I cannot connect to the database  because: ' . mysql_error());
  //-select  the database to use
  $mydb=mysql_select_db("yourDatabase");
  //-query  the database table
  $sql="SELECT  ID, FirstName, LastName FROM Contacts WHERE FirstName LIKE '%" . $name .  "%' OR LastName LIKE '%" . $name ."%'";
  //-run  the query against the mysql query function
  $result=mysql_query($sql);
  //-create  while loop and loop through result set
  while($row=mysql_fetch_array($result)){
          $FirstName  =$row['FirstName'];
          $LastName=$row['LastName'];
          $ID=$row['ID'];
  //-display the result of the array
  echo "<ul>\n";
  echo "<li>" . "<a  href=\"search.php?id=$ID\">"   .$FirstName . " " . $LastName .  "</a></li>\n";
  echo "</ul>";
  }