Carry out the following steps:

Let's start with the admin action of our customer controller:

public function actionAdmin()
{
  $model=new Customer('search'),
  $model->unsetAttributes();  // clear any default values
  if(isset($_GET['Customer']))
    $model->attributes=$_GET['Customer'];

  $this->render('admin',array(
    'model'=>$model,
  ));
}

The Customer model is created with the search scenario, all attribute values are cleaned up, and then filled up with data from $_GET. On the first request, $_GET is empty but when you are changing the page, or filtering by the first_name attribute using the input field below the column name, the following GET parameters are passed to the same action via an AJAX request:

Customer[address_id] = 
Customer[customer_id] = 
Customer[email] = 
Customer[first_name] = alex
Customer[last_name] = 
Customer[store_id] = 
Customer_page = 2
ajax = customer-grid

Since the scenario is search, the corresponding validation rules from Customer::rules are applied. For the search scenario, Gii generates a safe rule that allows for mass assigning of all fields:

array('customer_id, store_id, first_name, last_name, email, address_id, active, create_date, last_update', 'safe', 'on'=>'search'),

Then the model is passed to a view, protected/views/customer/admin.php. It renders an advanced search form and then passes the model to the grid widget:

<?php $this->widget('zii.widgets.grid.CGridView', array(
  'id'=>'customer-grid',
  'dataProvider'=>$model->search(),
  'filter'=>$model,
  'columns'=>array(
    'customer_id',
    'store_id',
    'first_name',
    'last_name',
    'email',
    'address_id',
    /*
    'active',
    'create_date',
    'last_update',
    */
    array(
      'class'=>'CButtonColumn',
    ),
  ),
)); ?>

Columns used in the grid are passed to columns. When just a name is passed, the corresponding field from the data provider is used.

Also we can use a custom column represented by a class specified. In this case we are using CButtonColumn that renders the view, update, and delete buttons that are linked to the same named actions and pass the row ID to them, so action can be done to a model representing a specific row from the database.

The filter property accepts a model filled with data. If it's set, a grid will display multiple text fields at the top that the user can fill to filter the grid.

The dataProvider property takes an instance of data provider. In our case it's returned by the model's search method:

public function search()
{
  // Warning: Please modify the following code to remove attributes that
  // should not be searched.

  $criteria=new CDbCriteria;

  $criteria->compare('customer_id',$this->customer_id);
  $criteria->compare('store_id',$this->store_id);
  $criteria->compare('first_name',$this->first_name,true);
  $criteria->compare('last_name',$this->last_name,true);
  $criteria->compare('email',$this->email,true);
  $criteria->compare('address_id',$this->address_id);
  $criteria->compare('active',$this->active);
  $criteria->compare('create_date',$this->create_date,true);
  $criteria->compare('last_update',$this->last_update,true);

  return new CActiveDataProvider(get_class($this), array(
    'criteria'=>$criteria,
  ));
}

This method is called after the model was filled with the $_GET data from the filtering fields, so we can use field values to form the criteria for the data provider. In this case all numeric values are compared exactly while string values are compared using partial matches.

Code generated by Gii can be useful in a lot of simple cases but often we need to customize it.