In actuality, the air in earth's atmosphere becomes thinner and thinner as you move towards outer space, but there is no finite line that marks where our atmosphere ends and space begins. However, there are several ways to describe how far one must go to be "out of Earth".

The line, which is 100 kilometers (62 miles) from the earth's surface, is often used as the internationally accepted border between earth's atmosphere and space. However, you must travel only 50 miles above the earth's surface to be designated as an astronaut. Finally, for a spaceship coming towards earth, it begins to feel the effects of the atmosphere at a height of 120 kilometers (74.6 miles) above the earth's surface.

So to answer your question simply, a good estimate for the beginning of outer space would be roughly 100 kilometers (62 miles).