If a firm were long 100 March 2008 Eurodollar contracts, it could get out of or offset this position by simply going short 100 March 2008 Eurodollars. Note that the underlying asset (Eurodollars), the contract month (March 2008), and the size (100 contracts) must be the same.
This is one of the features that distinguishes a futures position from a forward position—a futures position can be very easily undone by simply doing the opposite of what was done to create the position—buy if you previously sold, or sell if you previously bought.
There is a caveat. In the case of futures, you must offset your position at the same exchange where you initiated it, even if another exchange offers the same product. This is because each futures exchange has its own clearinghouse. So you cannot, for example, buy 50 crude oil contracts at NYMEX and sell 50 crude oil contracts at ICE Futures and expect the two to be offset.
This is very different for those used to trading U.S. equity options, where you can create a position at one exchange and offset it at the other exchange. this is because all options exchanges clear at the same clearinghouse—the Options Clearing House, or the Options Clearing Corporation (OCC).