I need to get from Schiphol Airport to Rotterdam Central Station. Is there a direct train? How much would a taxi cost?
There is a direct train, and it is easy to find from the airport. You don't have to go outside.
According to http://www.ns.nl/reisplanner-v2/index.shtml the one way trip will cost you €11.60. And you have two options per hour
Travelling by taxi would be significantly more expensive if you take a taxi directly from the airport. I can't predict the exact cost, but you should not expect anywhere less than €80,- (estimate, this is an absolute lower bound).
Unless paying by card (for which there are machines, with English as an option, scattered all round the concourse and even in the baggage collection area) there is a Euro 0.50 surcharge for a train fare bought at the counter (but no queues!) The platforms are below the concourse area and tickets are not available at that lower level. The trains are clean, fast, quiet, safe and I travelled in (to Den Haag – which is en route to Rotterdam) two months ago.
However the taxi from Centraal to my hotel was more than I expected so on return (with luggage to collect en route) I took a taxi. From the Schiphol side of Den Haag that was Euro 75, including a fairly generous tip
*. Rotterdam is 30% more mileage than Den Haag and with taxis from airports generally being more expensive than vice versa I would agree with
not expect anywhere less than Euro 80- without prior arrangements I would budget for Euro 120 in your case.
The journey time by 'normal' train should be about an hour plus however long you have to wait for a train and take to get from Rotterdam Station but by taxi should be similar.
* As an (irrelevant!) aside, my taxi driver explained en route that the many wind turbines, replacements for windmills I somewhat regret, are for pumping water rather than generating electricity for the grid. Seemingly the Schiphol area is metres below sea level and the airport name is taken from the days when the area was a harbour for ships that floated rather than flew.
There are number of high speedy train operated by NS International. It takes approximately 10 minutes with price ranging from 21 Euro to 34 Euro. You can check price and book ticket online at https://www.nsinternational.nl/en