Making a drop shadow is quite simple in gimp, but is a bit tricky sometimes.

First make a selection, this will be the area where your drop-shadow will be made.

I'm going to fill my selection with red.

Now, go to in the menu -> Filters -> Light and Shadow -> Drop Shadow...

That will open this dialogue:

There are many options, X and Y change the distance from the object the shadow is left/right and up/down, the values go positive and negative. Play around with them to your liking or purpose.

The default values make a drop shadow like this:

Maybe not exact to what you want, so playing around with the values, we can come up with something nice.

If we want to get more advanced we can add a layer mask to the drop shadow layer and mask off only the bottom part of the shadow (or erase the rest with the eraser if you want).

Or If you feel skilled with the paint brush you can paint a shadow from scratch as show below:

And in mixing techniques you can come up with convincing shadows for your design: