I've defined a layer to be used as a popup/flyout menu, but my page is still visible right through that layer. How can I change this?
If you don't specify a background either for a layer or for its content (eg. a table), then the layer is transparent. So yes, then you can see right through the layer.
Specify a background (either a color or an image) and your menus should be fine.
Another common issue is that the (menu) layer has a lower z-index than some other layer which effectively places it under the other layer. That way too, it can seem like you can see through the (menu) layer, while in fact the other layer is displayed on top of the (menu) layer.
Make sure the z-index ordering of all your layers is correct.