Cleanest way to empty shop vac?
Filter bags

One of the cleanest way to empty a shopvac is with a filter bag.  Most dust will be caught in your bag and not in the shopvac tank.  You just have to remove the bag and replace with a new one.  If you use your shopvac a lot, it can become expensive on the long run.
Cyclone Collector

Another solution is to add a separation stage to your shopvac.  That's usually done by adding a cyclone collector.  The idea is pretty simple, it's to collect bigger chips and dust particles in a regular trashcan or bucket and then send the rest in your shopvac. That way, you won't have to empty or clean your shopvac as often.  It can also be combined with the filter bags to reduce the amount of bags you use.
Extra reading on dust collecting and cyclones

Bill Pentz has done some extensive research and work on this subject.  Keep in mind when reading his site that he has developed some allergies to saw dust.
Phil Thien also has a separator lid.
You can also most likely buy a pre-made one online or at a local retailer.