What do you want to bury?
In my area, 4' deep is necessary to prevent freezing. 3' deep is required by code for power; but low-voltage lines (e.g. ethernet, fiber optic, telco, television) only have to be deep enough to avoid accidental destruction as the owner sees fit.
Clay can be a bitch. We live in glacial till; so we have layers of sand/clay. When you hit one of our clay layers, you need a pick to bust out little pieces. "Digging" is not an option. The conventional wisdom is to use a "ditch-witch" as described above. They can come equipped with a spool of conduit and a blade to dispense the pipe right behind the digger. After the conduit is in place, you just "blow" a string thru it with a vacuum cleaner; and use that to pull whatever.
There is a service here (actually required by law) called: "dig safe." One calls them and within a very few days, power, phone, cable, etc. show up and mark your designated area with chalk lines illustrating the path of their lines. It makes it fairly easy to avoid with a ditch-witch.