First you have to buy a shovel from Tom Nook for 500 bells. Then you have to find an X type thing on the ground. Then you stand next to it and press A or tap yourself.
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For a spade - Buy two spades, bury one shovel in the ground and then dig them up 24 hours later.
in the rivet ravine pay to dig area
you go to Beth and ask to go to any of the dig sites
You can buy it, or dig it up at Rainbow Canyon as a giant neutral-type fossil rock (Regular dig site, availible pre-ending).
U get it from the fossil maniac