How to build deck posts into clay soil
Post longevity:

Concrete, below frostline (varies with where you are), with a footing, reinforced with steel rebar kept 2" from the face of the concrete. Use brackets or pads to keep wood from touching concrete aboveground.

Hole: Cheap, or Lazy? 

Cheap - post hole digger (clamshell type) or mattock and shovel (depends how hard the clay is when you try to dig the hole - will vary somewhat with water content through the year.)

Lazy - equipment - excavator/backhoe, power auger, etc. - note - power auger needs to be on a tractor or similar to really be lazy - the ones you hand-hold seem to be quite a workout to use. And always be sure you know what is below before digging - call digsafe for official marking before you start, and attempt to determine what private services you may have in the area such as plumbing lines, sprinklers, exterior lighting wires, etc. 

Cheap and Lazy - You said a "ground level deck" so patio blocks right on the ground, no holes at all. If not quite that lazy a sand bed will help future performance of the surface some, but it may need to be taken up and regraded from time to time anyway.