Well, in the era we're discussing, there wouldn't be jackhammers. Mainly a bunch of guys with pickaxes.
Generally you just build a fire on the ground you want to dig up, possibly throw in some good sized stones to hold the heat longer. If the frost is deep might turn it all over once the flames have died down and bury those coals and stones so their heat is more contained and not just going up into the air, or have a second fire after you have dug out the thawed soil.