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.

I'll second that... one of the things that you might encounter is a tube that has been out of service for a long time will have quite a bit of gas leaked inside, and you might have to let the ion pump run for days to get the leakage current down to an acceptable level before turning on the rest of the circuitry. My friend actually ended up using a high voltage supply one particularly troublesome tube, but in the end we were able to get it going... it just needed a lot of ion pumping.

The bandwidth of the tube is VERY narrow (on the order of a few hertz, which means you have to be quite close on the frequency of the crystal oscillator before it can lock in.

You also want to be careful when adjusting for the Zeeman frequency to pick the right peak, or you will end up with locked to the wrong transition, and your clock will drift ,although in a very precise amount of drift ;-)

It's fun, once it works. It's easier the second or third time, of course.