Sometimes the pups already have roots. Take them with the pup if yours do.
Let the soil in the aloe pot dry. Remove the pups and place them away from bright light for 24 hours, or however long it takes for the cut end to dry. This is called 'callusing'. This is not necessary if the pup already has roots. If it does, just plant it at the same depth as it was originally. Cacti and succulents usually do best if transplanted dry. Let rooted pups stay dry for 2 or 3 days, then water thoroughly.
Place unrooted and callused pups in dry cactus/succulent potting mix just deep enough so they don't fall over. Usually, 3/4 of an inch to an inch is plenty. I sometimes use small stones to help prop them up. Don't water the soil for about 5 to 10 days. Watch the pups every day, and if you see any sigh of wrinkling, then give the soil a good soaking. Don't water again until the leaves just begin to look a bit wrinkled again. You will know new roots have formed when you see the pup sending up new leaves. They actually root pretty quickly, especially this time of year. Watch for new leaves to peek out within 2 or 3 weeks.
Aloes are desert plants. They're tough. Mostly they die from overwatering. Remember to allow your newly planted pups to adapt to outdoor sunlight if they've been growing indoors. In fact, I'd give them about 5 days in the shade even if they've been in full outdoor sun their entire lives. It gives the roots a chance to get established in the new container.