Aloes have a shallow, spreading root system, so when it is time to plant, propagate, or repot choose a wide planter, rather than a deep one. Use a planter with a drainage hole, or provide a 1-2 inch layer of gravel in the bottom of the pot to ensure adequate drainage. I find terra-cotta pots are perfect for aloe because they don't retain the extra moisture that could damage the plant, but, if you are careful not to over water any planter will do. When you pot your aloe offshoots, or the main plant, use regular potting soil with a extra perlite, granite grit, or coarse sand added. You may also use a packaged 'cacti mix' soil. I have had success with a composted ‘cow manure’ product. Dampen the soil before potting. The plant won’t require more water for a couple of weeks. Then pierce the soil with a fork, breaking up the hard surface, down to about two inches. This allows the soil to better absorb the water. Water lightly until it comes out of dormancy in the spring. Fertilize yearly, in the spring with a dilute (half strength). Aloes are propagated by removing the offsets which are produced around the base of mature plants, when they are a couple inches tall (or larger). I usually let them get 4 to 6 inches. Aloe plants love bright sun, but will do fairly well in medium light as well. Allow the soil to dry between watering and water less in the winter than in the warm months. They like being pot bound in my experience, and may be divided each spring or before if you have a lot of baby plants in the pot. The aloe is a succulent plant, with leaves that can hold water for long periods at a time. Too much water can rot the plant, and it would take the most severe drought to dry it out. The plant's only other enemy is cold. It will do quite well next to a window with even minimal light, but it prefers bright, indirect lighting.
An aloe plant is a welcome friend in the kitchen. Potting aloe is a great children's project by the way. The plants are easy to handle, and hardy enough for little hands to replant.