Layers

Layers come in three flavors, only two will be covered below. Raster - pictures and other fixed-size graphics are rasters, and Vector - vectors are resizable without risk of pixilizating (usually text). The third, adjustment, allows the ability to adjust images by using masks. Since such adjustments are a separate layer, all changes in the image can be instantly removed by removing the layer. Since such adjustments are available for use directly on any raster layer, it won't be covered separately here.

Adding/Selecting layers: It's possible to add layers directly through the "Layers" menu, but it isn't generally necessary - usually you add a layer by adding an image as a layer. If you load a picture as your starting point, it will be your "background" layer. A lot of manipulations (including many of the effects) are not available for backgrounds, so if you intend to apply effects, promote the background to a layer (it's at the bottom of the "Layer" menu). 

You can select which layer to work on through the "Layers" menu. Each layer is a separate image, so you can apply effects only to that layer, leaving the rest of the layers (and their contribution to the overall pictures) intact. If your layers represent objects in your picture, clicking on them selects the layer in which they lie. It's easy to forget what image is in what layer - under "Layer/Properties" is the ability to give meaningful names to your layers, so you can keep them straight..

Adding a raster layer through cut/copy and paste:  In order for this to work, you MUST be working in 16 million colors! Look at the picture properties at the lower right hand corner of your workspace (see Editing for details). If you aren't, select "Increase Color Depth" from the "Colors" menu, and click on "16 Million Colors." Select any image you wish to add as a layer - it can be another image, or even a portion of the image on which you're working (use the "Select" tool - see Editing for details). Select "Edit/Copy," select your target image, then select "Edit/Paste..." and click on "As New Layer." You will automatically be given the "Mover" tool, with which you can position your new object/layer exactly where you'd like it.

Copying and pasting directly from the image itself is how you can remove (by covering) or move parts of the picture. See the Layering Example for an example of how this works. See also the Text Layer example for how to add a vector text layer.