If you have experience with analog and digital electronics it's not very hard. Atomic clocks were part of Hewlett-Packard's glory days and in that era the user got full documentation, schematics, theory, trouble-shooting guides, etc. The manuals are all still available online or on eBay.

There is also the time-nuts mailing list where hundreds of us share questions and experiences with repairing and running old atomic clocks. The archive is 20 years deep so there's lots of good info on bringing dead cesium and rubidium clocks back to life:

http://leapsecond.com/time-nuts.htm

The one problem is if the old cesium clock you buy has "run out of gas". The quantum mechanics physics experiment encapsulated inside the tube is a one-way street so once the tube runs out of cesium one has to replace it. The typical solution is to buy a few cesium clocks over time on eBay and mix parts until you have one that works well.