We raised brown garden snails, which are a commonly considered to be a pest species. We kept them in gallon-sized jars (sun tea jars work well) with a fabric (light cotton) cover. The cover was simply held on with a rubber band. We tried moist soil in one container and wet paper towels in the other. The paper towels were easier to clean and the snails sometimes used the towels for food. We were vigilant to keep the towels moist.
The soil was more of an issue, because we soon had an overgrowth of springtails and sowbugs that we had accidentally added with our garden soil. The soil was also harder to keep free of rotting vegetable matter. (Hence the extra critters). Snails need to be cleaned frequently.
You will need to add sources of calcium, like egg shells. We gave the snails egg shells that we washed out. We also gave them a number of different leafy vegetables.
The snails laid their eggs in the paper towels or under the soil. In no time we had a lot of snails (you probably should have an “exit plan” such as friends that are willing to take some off your hands). Taking care of snails and watching their life cycle was a great way to learn about a creature so different from our fuzzy pet friends.
The book Snailology by Michael Elsohn Ross, Darren Erickson (Illustrator), and Brian Grogan (Illustrator, Photographer) is also a wonderful resource.