If you pass the JSON in your post to json_decode, it will fail. Valid JSON strings have quoted keys:

json_decode('{foo:"bar"}');         // this fails
json_decode('{"foo":"bar"}', true); // returns array("foo" => "bar")
json_decode('{"foo":"bar"}');       // returns an object, not an array.

$json = '{"apples":"green","bananas":"yellow"}';
print_r(json_decode($json, true));

Will be:

Array
(
    [apples] => green
    [bananas] => yellow
)

I'm passing true in the json_decode function, because othertwise it's a stdClass object. Your choice what you like more.

//Edit:

His JSON string was invalid, thats why PHP couldn't convert it. Fixed one:

{
    "Parameter": {
        "LookupName": "EmailAddress",
        "LookupValue": "example@example.com"
    },
    "Columns": {
        "Include_CSV": "ProspectID",
        "FirstName": "",
        "LastName": "",
        "EmailAddress": ""
    },
    "Sorting": {
        "ColumnName": "FirstName",
        "Direction": "1"
    },
    "Paging": {
        "Offset": 0,
        "RowCount": 200
    }
}