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Scientists on Earth do incredible calculations and programing to make sure every ship reaches its destination. The first trick is sending the probe in the right direction and make sure it can slow down when it needs to. We call this astrodynamics. 

Then, scientists and engineers have a lot of tools they can control on the probe itself: thrusters and rotation wheels, for example, allow the engineers to pilot a craft from hundreds of thousands of miles away. This way they can make sure it stays on course. Once it gets close, it slows down and is grabbed by the planet's gravitational pull.

With good math, you can go a long way - to the edges of the solar system and beyond.