Build a small charcoal fire over the area you want to dig up. Providing there are no fire hazards nearby, the fire is an effective way to soften and even melt the frost layer and thaw out the dirt beneath. This will take some time, however, and you have to watch the fire closely.
Boil several gallons of water on your stove and immediately pour the hot liquid onto the ground. Repeat this several times over the course of an hour or two to thoroughly saturate the frozen ground with hot water. This will melt through the frost layer and make the dirt easier to dig into.
Use a pick to dig through the soil once it has softened enough to allow progress. The earth will become warmer and less solid starting about four inches beneath the frost layer, at which point a shovel may become feasible.