How do atomic clocks keep up with the Earth's rotation?

By the addition of "leap seconds" every few years.

The grandly named International Earth Rotation and Reference Systems Service (IERS) based in Paris, is responsible for keeping track of the gap between atomic and planetary time and issuing international edicts on the addition of leap seconds.

In recent years a leap second has been added every few years, slightly more infrequent than in the 1970s despite the long-term slowdown in the earth's rotation caused by tides, earthquakes and a host of other natural phenomena.

The last leap second was added at midnight on June 30th 2012. The next one will be in 2015.

The link also explains the difference of opinion in scientific/technical forums about the wisdom or otherwise of the IERS edicts.

They are usually kept in special cabinets which are fixed to the Earth's surface so they naturally follow the Earth's rotation.