This should be fairly simple, have a look at the Server-side example ServerApplicationBar.aspx.
In the aspx the ApplicationBar has 3 key properties relating to this:
The CustomizeMenuID is the ID of the Customize menu declared in aspx page. This is a standard Telerik menu.
The OnClientCustomizeClick event fires on the client when you click the clustomize button.
When you click the customize button we call the showCustomizeMenu method against the client-side ApplicationBar object. This shows the customize menu. When you click the menu it does a standard post back to the server using the OnItemClick="CustomizeMenu_ItemClick" server-side event handler. Once on the server we simply toggle the minimized state with the line:
this.MainApplicationBar.MinimizeRibbon = !this.MainApplicationBar.MinimizeRibbon;
The rest of the event handler deals with changing the menu’s image to toggle the display of the tick.
While you can do this via a post back I would suggest you look at the Client-side example ClientApplicationBar.aspx. This toggles the minimized state without doing a post back and so gives better user feedback.