|Tomatoes need at least a 5 gallon bucket to grow in, well-drained soil mix, full sun, and regular fertilizer. Buy the buckets at any home store or big box and drill six holes in the bottom of each one. I like a drill bit about 3/8" for this task. If you use a bagged potting mix with water holding crystals in it (most of the name brands do) drill another set of 6 holes around the sides of the bucket, 1 inch above the bottom. Put an inch of gravel or something like that in the bottom, put soil on top, plant and put in your tomato cage. Water each bucket by itself from the top for a couple of weeks and start fertilizing. The use of the kids hard shell swimming pool is meant to keep the pots watered. I always say (and it's true) that each time a tomato plant wilts, you lose. That means you water often enough to prevent wilting, not enough to keep the pots wet all the time. It's water, let dry out a little but not to the point of wilting, and water again. One reason the minimum is a 5g bucket, not the maximum, is the challenge of keeping big, healthy plants hydrated in limited soil volume. It can be done with an automated drip system on a timer easily enough and there's no possibility of creating a mosquito environment as there might be with the pool. If you're vigilant about the water level, though, it's a fine way to grow and water as many pots as will fit into the pool with plenty of sunlight and air circulation for each one. (Nobody's going to drag those pots in and out of the pool!) You'll adjust the amount and frequency as the plants grow as you would in the ground, but start like this: Put the buckets in the pool with just enough water to be taken in from the bottom (but below the holes along the side of the bucket). The pots should take up virtually all the water in 30 min, but no more than an hour. If it goes much quicker, you need more water. Much less, especially if the top of the soil begins to look wet, means you overwatered. Lower the water level next time.
If you don't mind using a good bit more water each time, elevate each bucket so when the pool is dry, air can circulate around the entire pot and prevent overheating that plastic. I also like that there's no chance Bermuda grass or other weeds can grow up through the drain holes into the tomatoes, peppers, or whatever else is growing in the bucket. I grow almost all my veges in containers, so I'd add bush squash and cucumber to the list as well as basil and eggplant.
Managed well, this can be a winning strategy.