Mid-day/afternoon is often considered the worst time for photography as the light's harsh but as we're in search of shadows you can ignore this piece of advice and head out with your camera while everyone else is still eating their lunch.
Shadows can give what would be a boring shot of an object/building depth and interest so make sure you take a look at everything and give objects you originally dismissed as a good photographic subject a chance. Shadows can also be used as a tool to lead the eye through the frame when they are reaching out across the floor towards the foreground of the shot.
If you're going to use both the shadow and the object that's created it in your photo don't clip the edge of the shadow as you'll end up with a messy looking shot. Also, check the frame to make sure your own shadow isn't trying to take centre stage.
You don't always need an object in your shot as a shadow on its own can create an unusual and dramatic shot. Geometrical shadows such as those created by lines of trees, fences and gates can work particularly well.
The darker/stronger the shadow the better the photo so try to use exposure compensation to give your shadow a little more oomph. This is a feature found on a variety of cameras from compacts to more advanced models such as the Olympus OM-D EM-1
where exposure compensation can also be used in Live View.
Olympus OM-D E-M1 - The whole package. In a perfectly-sized package. Click here for more information on the most advanced compact system camera ever produced. The E-M1 comes packed with technologies such as the enhanced Live MOS sensor, TruePic VII image processor, Dual Fast AF and extended WIFI controls.