The most common ways are:
1) Create a plane object that sits at your character's feet and texture it with a shadow texture. This can be tricky because black is used for transparency which means your shadow will actually be light grey. The "blob" method doesn't look particularly great but it does the job and doesn't take up a lot of resources.
2) The other method is to take a copy of your model (preferably an extreme low polygon version) and squash it 100% on the y-axiz using the SCALE OBJECT command. Then color it black and you've got a perfectly shaped shadow that can also be animated to mirror the casting object. This looks better than the blob method but still isn't really accurate plus it takes up more memory and polygons.
That's about all that's available to the DB user, hope this helps.