<Button Text="Open Name filtering UI" Clicked="openfiltering_Clicked"/>

<telerik:RadDataGrid Grid.Row="1" x:Name="grid"
                     ItemsSource="{Binding Items}"
                     AutoGenerateColumns="False">
    <telerik:RadDataGrid.Columns>
        <telerik:DataGridTextColumn PropertyName="Name"
                                    HeaderStyle="{StaticResource style}"
                                    x:Name="nameColumn"/>
        <telerik:DataGridNumericalColumn PropertyName="Population" 
                                         HeaderStyle="{StaticResource style}"
                                         x:Name="populationColumn"/>
    </telerik:RadDataGrid.Columns>
</telerik:RadDataGrid>

    private void openfiltering_Clicked(object sender, EventArgs e)
    {
        // generate the context for the column you want to open Filtering UI
        var context = this.grid.CreateFilterTapContext(this.nameColumn);
        // execute filtertap command for this context (the column you want to open filtering ui for)
        this.grid.CommandService.ExecuteDefaultCommand(DataGridCommandId.FilterTap, context);
    }