How do I wall mount this sink?
Looking at the top back of the sink, there are two screw holes provided, but these are for location not full weight bearing.

Having removed a similar sink in the past, there should be two (ornate) cast iron arms which may also double as towel rails which are secured to the wall and support the weight of the sink.

Another version would have two posts that came up from the floor to the side/front of the sink, there may be evidence of fixing points if you look - the picture does not show us. You might consider an under-sink cupboard with short support posts...

If you don't have those arms or posts then you will need to make something equivalent as you will not be able to rely on those two screw holes.

You might find some searching on google etc will provide images of similar sinks with the supports shown.