This tutorial is an updated version of Stauns' drop shadow tutorial. It will show you how to create simple drop shadows for just about any shape.
1. To start with, the shape you're creating a shadow for needs to be on a single layer, if it's not, then you'll just need to repeat the steps detailed here for each layer that requires a drop shadow. Here is the shape I'm going to use:
2. Next, you need to duplicate the layer. Select your chosen layer in the layers dialog, then click "Duplicate Layer". The new layer should now be active. Now check the "Keep Transparency" checkbox. The layers dialog should look like this:
3. With the duplicate layer still active, press Ctrl+A to select the entire image. Now select the bucket tool and open the bucket fill options dialog. In the "Affected Area" section, make sure "Fill Whole Selection" is selected. Go back to the image and click anywhere. The shape on the duplicate layer should now be filled with black:
4. Uncheck the "Keep Transparency" checkbox on the layers dialog, and blur the entire layer by Right-Clicking, and choosing Filters->Blur->Gaussian Blur (IIR). A setting of 10x10 should be sufficient. I repeated the blur step four times, but do whatever looks right for your image. I've hidden the blue shape layer in the next screenshot, so that you can see the blurred image properly:
5. Move the shadow layer behind the shape layer by using the down arrow in the layers dialog. Select the shadow layer, and then select the Move tool. Select the image and move the shadow layer down and right slightly. I used the arrow keys and moved the shadow down and right by 4 pixels each, in the following screenshot:
6. Either add a new, white layer behind the shadow layer, or you can fill the background layer with white using the fill tool. Either way, it should come out looking something like this:
If you'd like to play around with the original XCF file for this, then you can download it here.