There are only a couple of options when mounting a sink with a counter top
. The slide in models that sit on the counter top with a lip placed around it. There is also the under mount sink that is mounted underneath where the counter top is.
The popular metal ones of today were available but they were porcelain coated. They were almost always white in color, styles have changed quite a bit. The stainless kind is all the rage now. They are easy to clean and maintain they do not get etched as the porcelain ones used to and they are durable. They used to always be almost exclusively porcelain.
For many moons probably until the nineteen seventies they were actually freestanding and the counter space was separate from it. These were very utilitarian but not very practical.
Today a free standing one is the exception not the rule. Sinks that are drop in are dropped into a hole that is left cut out of the counter top. The under mount sink is mounted on the underside of the counter top, this is the preferred method because debris can easily be wiped off the counter top into the sink without getting caught up on the lip of the sink. Counter top space is considered a must have so the sink is really secondary to it.
Typically if it is a drop in model sink than the edges under the sink do not have to be polished or finished because no one will see them. It is more expensive to mount a sink as an under mount, because the edges of the counter top have to be refinished around the sink.
Installing an under mount sink will probably take a couple of people or one person if they own the equipment that is necessary to support the sink while it is being installed. The process of installation should not take any longer than a couple of hours or so. It is very easily mounted using hardware that usually comes with it.