Top mount sink. Under mount sink. Vanity top and basin
There are basically three types of vanity sinks available. Top mount, under mount and one piece vanity top and basin.

TOP MOUNT SINKS
Using a jig saw, and cutting template supplied with the sink, a hole is cut in the vanity countertop. The opening is slightly less than the actual size of the sink. A sealing compound or gasket is placed around to hole and the sink is lowered into the opening resting on a narrow rim. Once positioned in place it is held in that position by clamps installed from below. This type of installation is virtually always used for preformed laminated vanity countertops.

UNDER MOUNT SINKS
As the name already suggest the sink is installed and clamped in place from below. The opening for the sink is cut by the manufacturer and the edge of the vanity countertop material is finished in the same manor as the rest of the countertop. This type of installation gives a clean contemporary look but is more expensive than the traditional top mount method. A special silicone based sealant provides a waterproof joint between the vanity countertop and sink. This type of installation is virtually always used for countertops made from natural or man made stone.

WARNING. In some under mount installations the sink is set back a bit from the opening in the countertop creating a small overhang. This "out-of-sight" space should be kept clean at all times to prevent a build-up of dirt and/or germs. This potential heath hazard does not concern top mount sinks and one piece countertops as there is no hidden overhang and all basin surfaces are visible.