With most pedestals, the base is simply a support. The sink top usually has a couple of bolt holes cast into the china or cast iron. Use a couple of lag screws to attach the top to blocking within the wall. You do want to exhibit care so as to not damage the top when lagging it to the blocking. The top gets attached to the wall. The pedestal base simply supports the top.

Depending on the sink, there can be coordinating "holes" in the top and pedestal for the waste plumbing to smoothly connect from the drain tailpiece to the waste line in the bathroom wall.

Console sinks can be either/or. Some console sinks have simple legs that only provide vertical support for the sink top, with the top getting lagged into the wall like a pedestal top.

With other consoles, the leg assembly is more like an erector set cage, and the leg cross bracing can also screw into the wall for lateral support.

I have been looking into brass console bases, and Palmer Industries in Rhode Island seems to be the place to go for custom legs. You give them the measurements and photos of the undersides of your sink. You mount it as Mongo explained, then install the Palmer legs. I was quoted $820 for a set of legs that would go up to 32" wide. You cut them down to size on site. You can even measure once the legs are in place and get them to make you a bottom shelf for stacking towels or for baskets and such.

Here is a link that might be useful: Palmer

My Restore had bases and no tops.. I just want to warn you....if you drop something in the sink...a can of shaving cream for instance....then it breaks/cracks the sink and you get to replace it.