Some plants won’t grow from cuttings; ferns, bromeliads… Those ones are easiest to propagate by division. I find dividing plants to be much easier than propagating from cuttings.
Wait until you have a good size clump of the plant. You’ll need to get leaves and roots on each division. Some plants can be gently separated by running them under water to remove all the soil then gently pulling apart. Others you’ll need to cut apart with a sharp razor.
I start most of new plants in sphagnum moss. It seems to keep the moisture more consistent and I have less problems with fungus and molds.
I like clear containers so I can keep an eye on the roots and moisture.
Divided plants don’t need any special care, I bump them up into larger pots or plant outside as soon as I see new roots or leaves.