Since both methods are general methods for customizing the "navigator" (toolbar) functionality of jqGrid, the first parameter of these methods should refer to searching - i.e the parameter should be a string - "search".

$grid->setNavOptions('search',array(...));
$grid->setNavEvent('search','java_script_code_here');

By default, the searching feature is set to search on multiple fields. If you want to allow searching just on one field at a time, you can set the multipleSearch options to false.

Here is an example:

<?php
require_once 'jq-config.php';
// include the jqGrid Class
require_once "php/jqGrid.php";
// include the driver class
require_once "php/jqGridPdo.php";
// Connection to the server
$conn = new PDO(DB_DSN,DB_USER,DB_PASSWORD);
// Tell the db that we use utf-8
$conn->query("SET NAMES utf8");

// Create the jqGrid instance
$grid = new jqGridRender($conn);
// Write the SQL Query
$grid->SelectCommand = 'SELECT OrderID, OrderDate, CustomerID, ShipName, Freight FROM orders';
// Set output format to json
$grid->dataType = 'json';
// Let the grid create the model
$grid->setColModel();
// Set the url from where we obtain the data
$grid->setUrl('grid.php');
// Set some grid options
$grid->setGridOptions(array(
    "rowNum"=>10,
    "rowList"=>array(10,20,30),
    "sortname"=>"OrderID"
));


// add navigator with the default properties
$grid->navigator = true;

//but use single search
$grid->setNavOptions('search',array("multipleSearch"=>false));

$grid->renderGrid('#grid','#pager',true, null, null, true,true);
$conn = null;
?>