Sinks and drainers...confused!

[proverbial]

Hi,
I'm trying to plan a new Ikea kitchen and my head is wrecked with all the fiddly bits!
The fixation of the hour is with the sink. Many sinks now do not have attached draining boards, and I don't really see how that works. For example I like this sink here but fitted into a wooden worktop, how do you drain anything you wash? Doesn't too much water wreck a solid wood top?

Am I missing something really obvious or am I being dim? Please help!

Our new kitchen at work came with a sink set into a stainless steel worktop and no draining board. After a couple of days mess, I searched and found this drainer which sits on top of the surface and drains back into the sink.

You'd have to make sure it didn't end up with a damp patch underneath though, on a wood surface. I suppose if you always dry your dishes, you could put it away under the sink after you'd used it.

Personally, I'd definitely want a "proper" builtin draining board in my own kitchen though.