There is a bit of info regarding what tool use for on the game pagew and if you try to dig with empty hand in game, but in most cases it is up to you. Pick is not very efficient digging dirt, it is for boulders and bones. Shovel - is fast but can damage artifact if it was in tile you dug up, brush is slovr but artifacts comeup in perfect condition.
Which tile contains artifact(or boulder/bone) is not random and can be figure out by visual cues.
We will try to make that clear in future releases... Somehow :D