You can find it in NPC villages or underground dungeons. But the easiest way to get it is to mind regular smooth stone, because that produces a block of cobblestone.
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Inside a cave, find a rock that has a reddish-brown spots. Make a stone pick using cobble stone, same as a wooden pick but with cobble instead of planks. Finally, mine it!
You craft a piston with 3 wood on the top row, cobble stone-iron ingot-cobble stone in the middle row, then cobble stone-redstone-cobble stone on the bottom row. Lastly, you put a slime ball above the piston in the crafting table, and voilà! You have your sticky piston!
You make them out of wood or smooth stone (not cobble). The wood ones can detect items and mobs/players, the smooth stone only the mobs/players. You make them like this: xxx xxx mmx where x is nothing and m is wood or smoothstone
Mostly, they can be found next to lava.
When you mine regular 'smooth' stone, you get cobblestone. This can be converted back to smooth stone by smelting it in a furnace.