Before you even start ripping apart countertops or ordering a new vanity you must consider your options when it comes to vessel sinks. First and likely the most important is what material, style, color and shape. These items are important because it will allow you to determine the necessary height of the countertop, mounting method and countertop material. Something I am often asked is, "What is the ideal height of a bathroom vanity for a vessel sink?". My answer is usually, "personal preference", but to come to a decision on height you have to consider the height of most of the people who will be using the sink. Small children and short adults will find it uncomfortable if not impossible to use if the sink is to high, and tall people will have to bend over if the sink is to low.
Most bathroom cabinetry for regular under mount sinks are between 30 and 32 inches, plus the countertop. So if you have to decide if it is ok to bring the total height to over 36 inches (since most vessels are between 5 and 6" tall) or if you want to have a more realistic 30-32" total height. You may be in a situation where you do not have a choice, either you want to use the existing cabinetry you have or the cabinet you want only comes in a standard height. In this case you may want to consider recessing your vessel sink to reduce the overall height, which brings us to the two main ways vessel sinks are mounted.
There are essentially two main ways to mount a vessel sink, but to be more specific, there are two main ways to mount a bowl shaped or cone shaped vessel sink with a smooth outer surface that is NOT MADE OF GLASS. If you have a glass sink or square / rectangular / zen / oval sink then you are basically "stuck" with the above counter mounting method. The other method, which is effectively known as "recessing" allows you to lower the sink partially into the cabinet so only a fraction of the sink is above countertop level. This method requires that your sink be a non-translucent material and that the exterior of the sink be very smooth and even the whole way around in order to prevent gapping. The recessed method of mounting also allows for greater stability since the bowl shaped vessel sink is supported all the way around by the countertop, vs. being supported by a mounting ring, the weight of the sink, adhesive and the drain itself (or a combination of these) in the "above counter" method.