Avoiding Armageddon

A robotic probe will be launched in 2020 to rendezvous with the asteroid, testing the ability of its gravitational interactions to alter the body's orbit. The probe will also provide further tests of solar-powered ion engines, which can move mass efficiently (if slowly) in space. NASA hopes to eventually use these engines to pre-position equipment and supplies for manned missions.

After the probe identifies and removes a boulder from the asteroid using robotic arms, it will further examine how the altered mass balance influences the asteroid's orbit. Eventually, however, the probe will depart with its boulder, returning it to the cis-lunar orbit and studying it on the way. It's expected that the rock will be in place by late 2025, after which the manned mission will follow using NASA's Orion spacecraft.

NASA announces details of its asteroid redirection mission | Ars Technica

The Hollywood solution: Nuke it. The possible solution: maybe just move it a teeny-tiny bit.