Most Echeverias require bright light and do not thrive indoors unless they are near a sunny window, receiving hours of daily sun. They tend to come from high altitude habitat where intense sun is not accompanied by serious heat, and as a consequence they do not thrive in very hot desert locations or enjoy lots of direct sun during the summer in marginal climates. In mild climates most plants can take part sun or more year round without any problems.
Echeverias (and their intergeneric kin) enjoy excellent drainage and prefer a pot that is wider than deep. It can be helpful to know the eventual size of your plant, but when in doubt, choose a pot that is not much more than an inch or so wider than the rosette. Water well when the soil has gone dry at depth, but not much sooner.
Some plants are solitary while others offset profusely, and this behavior helps determine the best method for propagation. Offsets (the easiest way to go) can be cut and planted with about half an inch of naked stem, and they will root within weeks. Intact leaves can be placed on top of the soil and they will usually sprout a tiny new rosette and roots at the base. Seeds are vanishingly small, almost dust-like, but easy to collect from mature, dry inflorescences. They require overhead protection after germination until there is a recognizable rosette.
Echeveria is closely related to other mostly New World Crassulaceae (Pachyphytum, Graptopetalum, Sedum, etc.) and can create intergeneric hybrids with these plants. It cannot hybridize with another closely related New World genus of rosette succulents, Dudleya (mostly from the Californias), with which it is sometimes confused.