Here, Let me give you a generic layout:

This may be the easiest way to use ajax, I use this in my every project. First link the external ajax.js then you can use the below script.

I don't exactly know where you have done wrong base on your description, but this works for me even locally. One reason may be your #response isn't loaded yet when you execute the script.

ajax.js

function ajaxObj( meth, url ) {
    var x;
    if (window.XMLHttpRequest)
        { //New Browsers
            x = new XMLHttpRequest();
        }
    else
        { //IE5, IE6
        x = new ActiveXObject("Microsoft.XMLHTTP");
        }
    x.open( meth, url, true );
    x.setRequestHeader("Content-type", "application/x-www-form-urlencoded");
    return x;
}
function ajaxReturn(x){
    if(x.readyState == 4 && x.status == 200){
       return true; 
    }
}

Script Tag Request for Ajax:

var ajax = ajaxObj("GET", "functions.php");
    ajax.onreadystatechange = function() {
        if(ajaxReturn(ajax) == true) {
            document.getElementById("response").innerHTML=ajax.responseText;
        }
    }
ajax.send("titleA="+title);

Or if you prefer JQuery:

//You need to load jQuery first before using this
$(function() {  //This line means when document is ready
    var ajax = ajaxObj("GET", "functions.php");
        ajax.onreadystatechange = function() {
            if(ajaxReturn(ajax) == true) {
                $("#response").html(ajax.responseText);
            }
        }
    ajax.send("titleA="+title);
});

I have fixed the problem, rewriting your code from the start really does help. The problem was that in my javascript I was sending the title as just +title, i really should have changed this to title.value, this is why the php wasn't understanding what i was trying to send it. Thanks Daniel for all the help. I will display all my code below. javascript:

    function searchData() {
        var title= document.getElementById("titleA");
        var request= new XMLHttpRequest();
        request.onreadystatechange= function() {
            if (request.readyState == 4 && request.status == 200) {
                document.getElementById("response").innerHTML=request.responseText;                 
            } 
        }


        request.open("POST", "functions.php", true);
        request.setRequestHeader("Content-type", "application/x-www-form-urlencoded");

        request.send("title="+title.value);
    }

    </script>

The php:

if (isset($_POST["title"])) {
$title= $_POST["title"];

} $connection= connect();

    $username= $_SESSION["username"];

    $tableA= $username . "_Anime";

    $queryA= "SELECT * FROM Anime." . "`$tableA` WHERE Title LIKE '%$title%'";

    $resultA= mysqli_query($connection, $queryA);

    if ($resultA == false) {
        die("no results found");
    }


    $numRows= mysqli_num_rows($resultA);

    echo "<table class= 'tSearch'>
            <thead>
                <th>Title</th>
                <th>Alt Title</th>
                <th>Seasons</th>
                <th>Episodes</th>
                <th>OVA's</th>
                <th>Movies</th>
                <th>Status</th>
                <th>Downloaded</th>
            </thead>
            <tbody>";

    while($row= mysqli_fetch_array($resultA, MYSQLI_BOTH)) {
                echo "<tr>";
                    echo "<td>" . $row["Title"] . "</td>";
                    echo "<td>" . $row["Alt_Title"] . "</td>";
                    echo "<td>" . $row["Seasons"] . "</td>";
                    echo "<td>" . $row["Total_Episodes"] . "</td>";
                    echo "<td>" . $row["OVAS"] . "</td>";
                    echo "<td>" . $row["Movies"] . "</td>";
                    echo "<td>" . $row["Status"] . "</td>";
                    echo "<td>" . $row["Downloaded"] . "</td>";

                echo "</tr>"; 
            }

                echo "</tbody>";
            echo "</table>";

            mysqli_close($connection);

                if ($resultA == false) {
                    echo mysqli_error($connection);
                }