Step 1 – Pick Your Spot
You need level ground and access to power for the pump. The whiskey barrel has a round footprint about 2 ½-feet across, so you need at least that much space, and filled with water and rocks it will be heavy, so it has to be on solid ground.
Step 2 – Drill Out the Buckets

The hose delivering water from the reservoir (the whiskey barrel) to the top tier (the small bucket) has to pass through the bottoms of the buckets, so drill a hole in the center of both buckets the same diameter of the hose, in this case ½-inch.
Step 3 – Cut the Landscaping Fabric
This is the material you put down on the ground to keep weeds from growing through. In this case, we're using it to mask the grill grates, and to prevent the pebbles from falling through them. Cut 2 pieces: one to cover the large grate and one to cover the small. Cut a slit in the center to let the hose pass through.
Step 4 – Thread the Hose

The hose passes through every element of the fountain, so start from the bottom and work your way up. First, go through a hole in the side of a small milk crate (this will keep the buckets off the floor of the barrel), then go through the center of the large grate, the landscape fabric, the large bucket, the small grate, the second piece of fabric and the small bucket.

You want the top to be about an inch below the rim of the top bucket. It fits pretty snugly, but you can secure it with a hose clamp inside the small bucket if you want. The hose itself plugs the holes in the buckets well enough, so you don't have to caulk anything.

The bottom end of the hose attaches to your fountain pump. The whole stack of tiers is 2 ½ to 3 feet high, so you can get a pump rated to a 3-foot stream if you want just a little bubbler at the top. If you want a taller spout of water, get a pump rated to 6 feet and dial it in the way you want.
Step 5 – Set the Stack in the Barrel and Fill With Rocks

Put the pump in the barrel, then put the crate and the whole stack on top. Make it even and level and then start adding the pebbles. Spread them evenly across the large grate, hiding it completely and making it appear that the barrel is full of rocks. You can build the whole fountain without the grates and actually fill each container with rocks, but then it would weigh a ton and you'd be up to your elbows in pebbles.

Cover the second grate with pebbles. Fill the top bucket with the stones, using them to keep the hose secure and centered.
Step 6 – Fill With Water and Plug It In

You need at least enough water to fill each bucket and spill over into the next, so start your hose on the top tier and work your way down. Fill the reservoir with double the amount in the buckets, so the pump doesn't run dry after it's delivered water to the top two tiers.

Plug in the pump and adjust the stream. Watch how the water flows. You may want to shift things here and there so the water spills over the fronts of the buckets instead of the backs.
This might mean being ¼-inch out of level, but no one will ever notice because they'll be too entranced by the babbling waters and impressed by your handiwork.