Drop shadows are applied using Layer Styles. You have to select the object you want shadowed and copy & paste it onto a separate layer. Then apply the Layer Style Drop Shadow to that layer.
If you want to apply a drop shadow to an entire picture, as suggested above, enlarge the canvas first. Then duplicate the layer. On the top layer use the Magic Wand to select the border area and hit CLEAR to make it transparent. Then apply the drop shadow, which will then be visible on the bottom lower layer.
You can adjust the shadow by clicking on the little "f" in a circle on the active layer. You can change the direction of the shadow, the distance from the object, the inner glow, etc. using this. You can also use Layer>Layer Styles>Scale Style to change the size of the shadow. Layer>Layer Styles>Style Settings displays the same adjustment window that can be accessed by the "f" on the active layer.
Another way to create a shadow is to paint it on a new layer, using a Blending Mode on that layer to get the effect you want. Try Multiply, Overlay and other modes.
You can also use the Burn tool to darken an area to give the appearance of a shadow.
There area always multiple ways to create effects in Elements!
