Initially I turn the rim of the bowl reasonably thinly and evenly before using a Dremel type carving tool to carve each individual hole. It takes me a long time since I have to be careful when carving to try to ensure that the holes are spaced evenly and also that I don't end up with some very big holes and other tiny holes which wouldn't give the same effect. Finally I hand sand each hole in turn.
There are several tools available that can be used for the carving but they mainly fall into two types air-powered drills and mains powered drills.
When I do lacework bowls the random pattern of holes I carve are all done by eye but when I create the more elaborate and complex designs such as the tallship on the platter or the seahorses on the Sea Life Vase I mark the designs out first. I also often enhance the carving by burning parts of the design with a pyrography kit.
I have now released a woodturning DVD on this particular subject, called Lacework Techniques with Yvonne Arlott, which covers it in more detail including the turning and carving of the Sea Life Vase.