How do you get a shovel on Poptropica?

On Nabooti Island

First you have to get the flower at Blue Nile Falls. Then you trade it with one of the market vendors back in Nabooti, to get a turban. When you go to Giza, put the turban on and one of diggers will give you a shovel. (It also has writing on it.)

On Big Nate Island

There is no shovel. The dog Spitsy will dig up the Time Capsule.

Skullduggery Island

You get the Bone Shovel when you get the instructions for the buried treasure.

(see related question)