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What happens when you get close to a black hole?

The exact effects depend on the size and mass of the black hole. A "stellar-mass" black hole - a black hole that's a few times the mass of the Sun - exerts a strong "tidal" pull on any object that approaches its event horizon. That is the same effect that creates the tides on Earth: the gravitational pull on the side of the object that is closest to the black hole is significantly stronger than the pull on the opposite side, so gravity stretches the object and pulls it apart. (Tidal gravity is less pronounced for an object that approaches a supermassive black hole, because there's a gentler "slope" in the changing gravity field.) As seen from an outside observer, time appears to pass slower for an object that nears the horizon, and its light is stretched to longer and longer wavelengths.