Upside down bottle type of waterer is basically a waste of money, unless your dog is large. You are buying a big bottle or tank. It amazes me that people actually use these things in the office. I hate to change the bottle.
For pets that drinks less than a few liter of water, you can make a waterer in a minute, with things in your recycle bin.
The tube and cup is optional. Without these your pet drinks from open spaces of the "coffee container".
The two pieces design makes it universal. For large pets, you can use several soda bottles with almost fitting outer container, which all feed into a single drinking cup.
For small pets, you can fit a small cup inside the cage suitable for the size of the pet and the size of the cage. The large soda bottle can stay outside.
Determining the optimal size and optimal placement of waterers also lead to 2 pieces design.
You want cups to be small to save space, keep water fresher or waste less water, reduce dust, and reduce other rubbish such as litter, food residue and animal waste. On the other hand, you need some mass so your pet cannot topple the waterer.
You cannot use soft plastic bottles such as milk bottles. They cannot withstand the atmosphere pressure and will be squashed. Ordinary soda bottle will be tough enough.
You can use whatever means to make a hole, such as scissor or knife. I drill a pilot hole using a plastic drill. Then enlarge it using a wood drill. Holes have to be at least 3/8". Water will not come out of small holes at all. A larger hole allows the water and air bubbles to flow more easily. Water comes out and air comes in at the same hole, nothing you can do about that. I enlarge the hole using a rotatory drill bit for cutting plastic. But a scissor is as good as anything else.
The hole should be near the bottom to maximize the delivered water volume but enough water left to give the bottle and outer container some weight for stability. The height of the hole is also one of the variables to adjust the water level.
You can just refill the bottle at the hole so make it in a convenient place, perhaps with a 2nd hole next to it for air to get out.
Any cup will do but there may be a lot of requirements. It has to be the right size for your pet, can be fixed or cannot be toppled. I use PVC under sink drain pipes with a U section. Pets drink from one end and the "plumbing" at the other side. You can glue or use all the other methods to fix PVC piping.
As shown, you just need a tube, dipping into the outer container and the cup. You don't need to do anything as long as the tube ends are under the water line.
I use 1/4" vinyl tubes for small pets. I'm not sure if vinyl tubes are for potable water. But 1/4 tubes for connecting to fridge ice makers are readily available, but not as flexible as vinyl tubes. There are also PEX tubes surely for potable water, but I don't know how flexible they are at 1/4". For larger pets, you may want to use 3/8" or larger tubes for faster refill.
The simplest way to keep the tube in place is to drill a 1/4" hole (for 1/4 flexible tubes) on the wall of the outer container and the cup, above the water line. Then insert the tube through the hole into the water. Of course you can always use clips.
The water level at the outer container and cup need to be aligned. Otherwise the cup either overflows, draining all the water, or the water level in the cup is too low for the pet to drink from.
You can start by changing the height of the outer container little by little, such as using stacks of old CD/DVD cases. Then you fix the cup, find some objects to replace the CD cases with the same height, cut PVC tubes as legs for a stand, or make an adjustable stand.
To start, you need to fill the bottle, raise the outer container up so the cup overflows. This get rid of air in the tube. If this doesn't work, fill the tube with water fully or partially, then insert into the outer container and cup. Try again.
Refilling the bottle
When the cup cannot be refilled by the bottle, it's time to refill. In this case, lift the bottle up will not spill any water into the outer container. There's no water in the bottle above the water level line.
If there is water remaining above the water level line, some water will spill into the outer container and then into the cup, which may overflow a bit. You have to lift the bottle swiftly and turn it horizontally so the hole is at the top.
Fill the bottle at the hole, carry it horizontally back to the outer container. Turn it vertical and slip into the outer container in one swift maneuver. It's easier than turning a water bottle upside down, and with less spills. Kids can do it, which is the goal of the design.
As long as the ends of the tubes stay in water below the level line, the system will keep on working.
It's trivial to dismantle the whole system to clean. You may even microwave all the plastics.
For some reason you may not want to dismount the cup from time to time. It may be mounted at a hard to reach corner, or the dismounting need a lot of work.
To keep the water fresh, you may need to drain the cup after, say, vacation. Fill the bottle nearly full. You fill a short 1/4" tube (same size as the other tubes) with water. Dip one end into the cup and drop the other end below the cup. Water will drain from the cup and being replaced from the bottle. Small particles will be sucked out of the cup. For larger particles you can use a thicker tube.
To disinfect the system, I suggest to use perfectly safe H2O2, available in drug stores at 3% strength. Drain the cup until the water left in the bottle and the outer container roughly equals the volume of H2O2 you want to add. (A 50% mixture is often suggested for disinfection.) Then pour the H2O2 into the outer container. Stop draining the cup when the water level in it starts to drop. Leave the system for a while for the H2O2 to take action.
To rinse the system, refill the bottle to full. Keep draining the cup until the water level in cup drops. Repeat.