Components will naturally separate over time.
When the separatory funnel has been filled with a multi-component liquid that contains a mixture of liquids of differing densities, the different densities will cause the fluids to naturally separate over time.
The heavier substance (usually the desirable product) will settle on the bottom, while the lighter substance (usually a clear solvent) will remain on the top.
Think of oil & water.
To understand the effect, one need only know how oil and water behave when contained and given time, due to their different properties. Due to the vastly different visual properties of the components in the mixture, it will be very obvious when separation is complete!
Load from the top, drain from the bottom.
You can pour your mixture right into the top of the glass at the opening. Make sure that the stopcock (the plastic valve at the bottom) is in the closed position, so no liquid will drain out from the bottom until you are ready.
Once the two liquids have settled, you can drain the bottom component using the stopcock.
You can also shake the funnel (while fully sealed, of course) to agitate the mixture, or simply invert it multiple times. Of course be careful not to shake too vigorously, as emulsions can result.
In the case of excess vapor pressure, make sure you can properly vent the top.
Shaking increases the surface area of the liquids, allowing each solute to move to the solvent in which it’s soluble. They are immiscible, meaning they will not form an incorporated solution. The result is two visually distinct layers, easily visible through the clear glass.
The beauty of this system is that you can only drain your end product, leaving only the solvent behind in the separatory funnel. Done carefully, the results are remarkably effective. Make sure that when you open the bottom stopcock, you also open the top as well. This allows for the necessary pressure equalization for the process to occur as planned.
The unique, semi-conical shape of these borosilicate glass funnels aids in separation, and they are incredibly easy to identify. The sloping or slanted sides of the glass make identification of the layers a breeze. On the top, you have a standard, taper joint, which can either house a rubber stopper or another connection.
Be mindful of safety.
If you are dealing with caustic or possibly harmful vapors, always make sure that you work with separatory funnels in well-ventilated lab, under a fume hood. In case of excess pressure, do not aim the top of the separatory funnel at your body (or worse, your face), and be sure to release pressure regularly to prevent excess build-up.