Choose and prepare one of the clay recipes (or use store bought clay such as Sculpey clay). All of the recipes work fine and depend on the ingredients you have on hand. I prefer the last version

Air Dry Clay
Air Dry Clay #2
Air Dry or Bake Clay
Air Dry or Bake Clay #2 -- dries whiter than the previous version, but requires cooking

Form the clay into a bowl using one of two methods (option 1 is easier than option 2):

Option 1: Pinch Pot method

Roll the clay into a ball
Stick thumbs into the center of the ball, pinching the sides to make a hollow (you're making a bowl shape, not a donut)
Flatten out the bottom of the ball to make a nice flat surface for the bowl (so it will sit sturdily on a table without risk of it falling)
Let air dry or bake dry depending on the type of clay you are using.
Use acrylic paint to decorate the pot however you like or leave it natural
Let dry

roll clay into a ball

pinch hole into the
center to make a bowl

I didn't paint mine,
but you get the idea

Option 2: Coil Pot method

Make a flat "pancake" of clay. This will be the bottom of your bowl.
Roll remaining clay into long snakes
Coil the snakes around the pancake of clay, building up the pot as you go.
You'll need to squeeze the snakes onto the pancake and onto each other a bit so they stay together when the project dries
Let air dry or bake dry depending on the type of clay you are using.
Use acrylic paint to decorate the bowl however you like or leave it natural
Let dry

roll a snake from the clay

I didn't paint mine,
but you get the idea

DLTK's Bible Crafts for Kids Jacob's Bowl

Materials:

Instructions:

Option 1: Pinch Pot method

Option 2: Coil Pot method

Printable version of these instructions

DLTK's Bible Crafts for Kids
Jacob's Bowl