What method was used in the roman empire to choose a new emporer

Once emperor and without an obvious heir, he had adopted Augustus. He may have been the first to choose a successor and call it hereditary succession, but he was not the last - Claudius sidelined his own son in favor of Nero, while Nerva "adopted" Trajan to ensure a smooth successio

The people voted for new emporers (and god i hope I'm not wrong cuz if not I'm just gonna sound stupid)