How do we fit a pedestal sink top onto a vanity base?
This is not a trivial project, as apron front sinks have straight edges on the front sides and bottom.

2 cleats should span under the sink to support the weight.  They should be sturdy enough to make the cradle, perhaps 1x3 or 1x4, oriented like joists.  You could reinforce the cabinet sides with the same size boards laid flat and extending to the cabinet bottom (like posts).  Using two pocket screws on each end of the joist would give you a bit of adjustability. Just don't drive them home until you're happy with the positioning.

The side cuts and top cuts should be back cut to make final shaping easier.  Making a foam template will be helpful and easier than sanding the top.  Blue or pink EPS foam at 1 inch should fit your needs.  A jig saw, belt sander, and perhaps a rotary tool ( like Dremel) will be most useful.  

Final affixing of bowl to top can be done by setting in a bead of sealant-caulk along top and front and perhaps a dot on each joist.