The same way(s) it does anywhere else...
It's a bit of an urban legend that water goes down the sink/toilet 'the
other way' in our hemisphere. Basically no one pays much attention to
which way the toilet drains until they are told it is going the 'other
way' - at which point they go "Hey, that's amazing!" and intend to check
again when they get home, by which time they've forgotten which way it
went in the other hemisphere.
However, if one tries out half a dozen different sinks and toilets - and
you may not even have to leave the house to do this - you'll see that
it's pretty much random, or more to do with which tap was used to fill
the bowl (for sinks).
Big storm systems do rotate the other way in our hemisphere - and if you
had a sink the size of a large lake with a *huge* plug hole it would run
down the other way to a similar oversized sink.
But things the size of sinks. Too small and local effects (like the
swirl from the water going in) take precedence.
There is a trick you can do at the equator, involving buckets - stand on
the equator, with a bucket (with plug), turn to the southern hemisphere,
the water will swirl out one way, turn to the northern it swirls the
other way - I think this was in one of Michael Palin's travel series.
It's all to do with the swirl imparted by the turning.
Unfortunately I was unaware of this when I crossed the equator[1]
otherwise I could have done some fun experiments.
--- Derek
[1] over land - I've crossed the equator several times in planes, but
they frown on experiments involving buckets of water in flight.