At scouting we build a frame from wooden poles, as scouts use when they do their pioneering badge, but any structure strong enough to hold the weight of the water would work. (Damaged pallets would be my choice, those that can not be turned in for a refund but if you use your pallets whole you can even get refunds for those used.)
The shape you want is that of the pool you showed in the question, but as the frame will be less specific, you will want to build it more sturdy, from wood it will get bigger.
Our scouts used the water on hot days as a small pool, but we used to leave the pool over to the next days on camp if the weather was going to stay hot, sometimes to the next weekend.
Cover the frame with old traps if you have them, to cushion the good one you are going to use for the waterproof layer.
Get a new tarp that is big enough to do the job, place it carefully and make sure you fold the corners such that the edge of the trap comes up to the top, all of the edge and the corner.
If your wooden structure comes higher than your expected water level, you can secure the edges of the trap with nails, I would prefer to use the rings in the edge and rope to secure it on the outside of the structure, in a way that does not damage the tarp.
If you do not trust the tarp or have to use an old one, you can use ductape on all places where you fear water will escape.
In the 'paint' part of the building supply shops you can sometimes buy clear plastic sheets to protect your furniture. If you can buy a heavy duty one which is as big as your tarp you can use that as an extra layer, which will add a water containing layer and will keep your tarp free of mud for later use. Whether it is needed depend on the structure of the tarp and whether it had been used before and whether you want to use it after.
If you need to store more than you can do with one tarp, you can make a multi pocket 'pool', each pocket the size of the tarp.
No digging needed and you can re-use your wood and tarp(s) after this project.