Which Berlin Airport?
 

I plan on staying in Berlin, near the main train station. I will be flying from Berlin to Amsterdam. What is the nearest airport to the main train station that will allow me to fly from Berlin to Amsterdam?

The nearest will be Tegel airport.
A cab will cost you around €15 and needs appr. 15 minutes.
Or you take the TXL bus for bit less than €3 from the Washington Square side of Central Station. The bus runs every 10-15 minutes.

If you find a cheaper flight from Schönefeld airport it is also no big issue.
There are two trains per hour which cost some €3. It just takes a little longer (appr. 30 minutes, plus 10 minutes walking under a covered walkway from the airport's train station to the terminal buildings).
Taking a cab would be more expensive - up to €40, depending on traffic.

Bookmarking

as in your other thread it will depend on WHICH airline you are using as to which airport. Tegel is closer to SOME parts of Berlin but not ALL of them.

My comment took into account that OP wrote that he/she plans to stay in a hotel near the central railway station.
So Tegel is the closer airport from that location.

Well done answering the question asked, Cowboy. It beats presuming the OP doesn't know the question they asked.
Tegel is closer to Schoenfeld and Tegel has flights to Amsterdam. Done