If you find you cannot dig at the red crosses you find around the land then the problem may be you have lost or sold your PickAxe. There is another tool called a Pick but this is more like a rake or hoe and cannot be used for digging successfully at the red crosses. If you have the correct tool all you need to do is stand on a cross and press the Action button. You will dig three times then something will be unearthed. If you try this with just the Pick you will dig endlessly with no success.

If you lose your pickaxe then it is possible to get another through the cheat mode:

Press C to bring up your stats.
Type in m a r v i n.
Press escape.
You will see Marvin Mode written in the top left corner.
Press F2 to bring down the console
Press i (for insert) then type in ITMW_2H_AXE_L_01
This will spawn a new pick axe in front of you on the ground.

It is advised to exit cheat mode afterwards. To do this, enter the stats screen again with c key then type in 4 2
You should see a message like "what is the question"

Now pick up your pickaxe and dig.