The photo above shows citrus swallowtail caterpillars in a variety of stages - typically the first three or four stages resemble bird droppings, later turning green in the final stage before pupation. When disturbed, swallowtail caterpillars project a fork-shaped gland from above their head, known as an osmeterium, which indicates to predators that they are distasteful or toxic, and releases a particular scent - it smells quite sweet to me but others report a foul smell. Nonetheless, this is rare in captivity, even when handling the caterpillars, and poses no danger to humans!
After about 3 or 4 weeks, the caterpillars will be fully grown and ready to pupate. At this point, they will secure themselves to the host plant or sides of their enclosure. Unlike many other butterfly species which hang upside down to pupate, the swallowtail caterpillar constructs a sort of sling out of silk, and pupates facing upwards.
I would recommend leaving the pupae in situ, as there is no need to move to another enclosure - they will do very well under normal room conditions, however would benefit from misting daily to avoid drying out. The adult butterfly will then emerge about 3 weeks later - this part can be really fun as you get to see the different varieties of swallowtails, which can be spectacular. You can also reference the care guide for pupae and cocoons here.
Adult butterflies can be cared for according to this guide. They are very straightforward, simply requiring ample space to fly and a food source.