Object Operation tab is an contextual tab and it bound to the map window. It will be shown on the ribbon only when the active window of the application is the map window. The most common geometry object in the map drawing are points, lines, regions and texts. Several kinds of drawing methods are provided.
The drawing of geometry objects can be done on editable layers, you can set several layers as editable, but when creating point, line, region or text objects, they will be created on the currently selected layer. So, if you want to create new object for a layer, click the layer in the layer manager and set it as the current layer.