Hopefully the picture is gives you most of the ideas on how to make this. I wanted to point out a few things I learned:

The mason jars did not pour well with just the glass part. I epoxied two lids back to front, and screwed that on -- this turned out to have a much cleaner pour. However when I added soap to create bubbles, even that wasn't sufficient. The water started going backwards along the mason jar, creating a mess of water outside of the tray.
The pipes were connected by a t-connector. There turns out to be a cute bit of fluid dynamics that shows up with this configuration. As long as water is flowing and the height of the two outlets are the same, the water should come out of them evenly. But until water is flowing, the maximum height of the tubes needs to be compared. The pipe with the lower maximum will start having water flow first, and then the water will only go to the maximum height on the second. So, to ensure that both have water flowing, keep the maximum heights the same.

Supplies

The pump is a SmartPond 155 Gallon per Hour pump from Lowe's. This was more than enough pumping; I put it on the lowest setting.
The pump has an interesting sensor that decides when the water level is too low. I found that if I took the side covering off, filled water just above the water pump, and then put my finger in front of the sensor (without even touching it!), the pump would turn on. Otherwise, it would stay off until I put enough water on top of it. I think there's something capacitive going on, as random items in front of the sensor didn't turn it on, but putting foil in front of it did.
Pipes (1/2 inner diameter for this pump)
Pipe t-connector
Wood
Tea pots or mason jars
If using mason jars
Mason jars
The mason jars are duck taped onto bent pieces of metal. I used LSTA 1-1/4 in. x 9 in. 20-Gauge Galvanized Strap Tie
Mason jar lids
If using tea pots
Tea pots
Clear string, to hold them up
Hot glue: keeps the mason jars or teapots in place. The teapots get glued to the clear string!
Soap

Step 1: Build the Wooden Structure

You'll need two pieces of wood that are cut at 45 degree angles. the others can just be longer pieces of wood. The piece of wood standing straight up is one of the standard 4x4's. The 45 degree wood pieces need to have a specific length: sqrt(2) * the height of the 4x4. If not, the 45 degree angles will be incorrect.

Step 2: Bend the Metal Strips

If using the mason jars, bend the metal strips to wrap around the mason jars at the desired angle.

Step 3: Epoxy Mason Jar Lids Together

The mason jars by themselves don't pour cleanly. But when water comes off the lip of a mason jar lid, the stream is nice and clean. I tried hot glue, but it was too fragile. Make sure that epoxy is covered all the way around the Mason Jar lid. And compress the two together with some weights on top while it dries. The important thing is that there are no gaps, because otherwise water will drip through this connection.

Step 4: Suction the Pump Onto the Bowl, and Connect the Pipes

The pump has suction cups on the bottom. You can simply press this firmly in the center of the bowl to have it stick.

Then, cut the pipes to the proper length. Connect them to the pump, as well as to the T-connector.

Step 5: Assemble and Add Water

There will be lots of tweaking to make sure that water is pouring properly and not dripping. This may take several attempts. Note that if you add soap later, the way the water pours will behave differently. It seems to stick more to the containers that it's pouring from.

Step 6: Turn on the Fountain

In my case, the pump didn't turn on even when there was water covering it. The problem was there wasn't enough water above it. By putting my finger (or aluminum foil) in front of this sensor, it got it to turn on. To make things more aesthetic, add soap to make bubbles so that the pump and foil are not visible.