If you shoot the bullet off the back of the train, the bullet will still be moving away from you and the gun at 1,000 mph, but now the speed of the train will subtract from the speed of the bullet. Relative to the ground, the bullet will not be moving at all, and it will drop straight to the ground.
What's true for bullets, however, is not true of some other things that you might "shoot" from the front of the train. A great example is sound waves. If you turn on the stereo in your living room, sound waves "shoot out" of the speaker at the speed of sound -- something like 700 mph. The waves propogate through the air at that fixed speed, and they can go no faster. So if you put a speaker at the front of the 1,000 mph train, the sound waves will not depart the train at 1,700 mph. They cannot go faster than the speed of sound. This is the reason why planes traveling faster than the speed of sound create sonic booms.