I keep mine in dirt, so it'll be slightly different. After they bloom, I just leave them in the pots and growing for several months (they need to recover). Then I take the pots in the garage and put them in a dark place and leave them mostly dry till the amaryllis go dormant. I leave them dormant for 10 to 12 weeks (or until they start growing on their own if I forget). If they need to be divided or repotted, I do this while they are dormant. Then I bring them out to the sun again and water/fertilize (if they weren't repotted) and let them do their thing. I have some that I've had for 10 years or more that way. Most of the ones I lost were due to raccoon attacks or slugs damaging the bulb.
You can pull off the baby bulbs and pot them up seperately. They may or may not bloom the first year or so. If the mother bulb has gotten too big, you can cut it into pieces and plant each piece to start a new plant. These won't bloom this year.