The hanging drop and wet mount techniques allow for observation of living organisms. The wet mount tend to dry out quickly under the heat of the microscope light; it is simpler to perform than the wet mount, but it is useful for short-term observation only. The hanging drop is a more complex technique, but it allows for longer-term obervation and more reliable observation of motility.
These techniques are usually performed without the addition of any stains; therefore, the organisms can be difficult to see. Reduce the illumination on your microscope as much as you can while still allowing yourself enough light to observe the organism.
If you use these techniques to observe motility, be sure you can tell the difference between motility and brownian motion. Vibration of the cell is caused by the cell colliding with water molecules. True motility allows the cell to move in different directions and across larger areas.
Refer to page 112 of your lab manual for a more in-depth discussion of these techniques.