Roll over the image to the right. The first image has been 'distressed' in Photoshop, and the second image is the original Illustrator artwork.
Here we've got a standard oil barrel which we drew in much the same way as the Terracotta Pot or Chess Piece. The Stroke Colour is #2B793C to match the logo.
Copy and paste the logo below into Illustrator, make it into a Symbol and lay it onto your object using Map Art.
To get the recessed 'filler cap' on the top of the barrel, I exported the Illustrator artwork into Photoshop and, with the filler cap left on its own layer - just as I drew it in Illustrator with the Ellipse Tool - I applied a Bevel & Emboss layer style to that particular layer in Photoshop.
While I was in Photoshop, I created a new layer below the 'barrel' layer and drew a simple shadow.