We had our bathroom remodelled and just had the sink mounted in a marble vanity unit which was attached to the wall. We decided (or more truthfully, "she who must be obeyed" decided) that we needed some storage underneath so I had to come up with a way of retro-fitting a cabinet without making too many new holes in the tiles.
This was a very easy build using no complicated joinery or other techniques. Although I did use a table saw to make some of the cuts I could easily have just used hand tools.
It won't win any awards for carpentry or design but it works and looks ok.