UPDATED:
Starting with version 14.2, GridView provides the built-in Search / Find Panel functionality with the capability to locate it outside grid boundaries. This allows accomplishing a similar task with less effort and does not require so much extra code. See the ASP.NET Data Grid: Enhancements post to learn more about this new functionality.
The example demonstrates how to implement an external filter for the ASPxGridView control. To accomplish this, handle the ASPxGridView.DataBinding event and specify a value of the ASPxGridView.FilterExpression property by using the BinaryOperator/GroupOperator types based on values of external editors. To rebind the grid, we perform a callback via the ASPxClientGridView.PerformCallback method.
See also:
How to implement an external filter for the ASPxGridView (ASPxGridView binds via postback)
How to filter ASPxGridView bound to SqlDataSource by using an external ASPxComboBox in Template