Send array with Ajax to PHP script

Encode your data string into JSON.

dataString = ??? ; // array?
var jsonString = JSON.stringify(dataString);
   $.ajax({
        type: "POST",
        url: "script.php",
        data: {data : jsonString}, 
        cache: false,

        success: function(){
            alert("OK");
        }
    });

In your PHP

$data = json_decode(stripslashes($_POST['data']));

  // here i would like use foreach:

  foreach($data as $d){
     echo $d;
  }

Note

When you send data via POST, it needs to be as a keyvalue pair.

Thus

data: dataString

is wrong. Instead do:

data: {data:dataString}

 dataString = [];
   $.ajax({
        type: "POST",
        url: "script.php",
        data:{data: $(dataString).serializeArray()}, 
        cache: false,

        success: function(){
            alert("OK");
        }
    });

http://api.jquery.com/serializeArray/

Data in jQuery ajax() function accepts anonymous objects as its input, see documentation. So example of what you're looking for is:

dataString = {key: 'val', key2: 'val2'};
$.ajax({
        type: "POST",
        url: "script.php",
        data: dataString, 
        cache: false,

        success: function(){
            alert("OK");
        }
    });

You may also write POST/GET query on your own, like key=val&key2=val2, but you'd have to handle escaping yourself which is impractical.

If you have been trying to send a one dimentional array and jquery was converting it to comma separated values >:( then follow the code below and an actual array will be submitted to php and not all the comma separated bull**it.

Say you have to attach a single dimentional array named myvals.

jQuery('#someform').on('submit', function (e) {
    e.preventDefault();
    var data = $(this).serializeArray();

    var myvals = [21, 52, 13, 24, 75]; // This array could come from anywhere you choose 
    for (i = 0; i < myvals.length; i++) {
        data.push({
            name: "myvals[]", // These blank empty brackets are imp!
            value: myvals[i]
        });
    }

jQuery.ajax({
    type: "post",
    url: jQuery(this).attr('action'),
    dataType: "json",
    data: data, // You have to just pass our data variable plain and simple no Rube Goldberg sh*t.
    success: function (r) {
...

Now inside php when you do this

print_r($_POST);

You will get ..

Array
(
    [someinputinsidetheform] => 023
    [anotherforminput] => 111
    [myvals] => Array
        (
            [0] => 21
            [1] => 52
            [2] => 13
            [3] => 24
            [4] => 75
        )
)

Pardon my language, but there are hell lot of Rube-Goldberg solutions scattered all over the web and specially on SO, but none of them are elegant or solve the problem of actually posting a one dimensional array to php via ajax post. Don't forget to spread this solution.

dataString suggests the data is formatted in a string (and maybe delimted by a character).

$data = explode(",", $_POST['data']);
foreach($data as $d){
     echo $d;
}

if dataString is not a string but infact an array (what your question indicates) use JSON.