How does the Federal Reserve remove money from circulation? I was watching a video about what gives money its value, and they say it's the total number of bills in circulation.

The Federal Reserve can print or remove money from circulation. But if somebody owns that money, they can't just take that money away right?  So how do they take money out of circulation?  Is there a limit on how much they can take out?
One of the Federal Reserve's (the Fed) primary policy tools is the Federal Open Market Committee (FOMC). Through open market operations the Fed can buy or sell securities on a secondary market. By buying securities they bring new money into circulation, by selling securities they take money out of circulation. 
Thus the Fed has a direct influence on the so called monetary base (M0, consisting of currency in circulation and reserves held by banks at the Fed).

It is true that the Fed cannot take the $-bills out of your pocket, but they don't have to. The Fed trades in securities, and every security has a price. Hence, if the Fed wants to take money out of circulation they "buy" dollars, by selling securities. At the market price there will by definition be people who are willing to give their money to the Fed in return for securities.

The value of money is determined by numerous factors beyond the monetary base (e.g. the money supply M1,M2,M3..., exchange rates) and is a concept harder to grasp, because value can be defined in various ways (as opposed to the "price" of money). But I think that goes beyond your question.