Think of them less like ghosts from traditional ghost stories and more like reincarnations, anonymous. While, yes, in some cases, they are spirits inhabiting tangible bodies (shuppet and banette, for example), many more have actual bodies with real organs—including, well, reproductive organs. They’re simply imbued with a spiritual energy and the memories of their most recent lives (as well as, in some cases, the ability to become intangible), so they’re not literally ghosts.
So yes, ghosts simply reproduce the way most other pokémon do. In the cases of shuppet, banette, or any other pokémon possessing a body, they do this by manifesting the organs they need to perform. Putting it another way, the bodies that shuppet and banette inhabit didn’t originally look the way they do as pokémon. Rather, the spirits that control them change them to suit their needs—including reproduction.
Should you be wondering, yes, this also means that pokémon such as yamask or phantump (those that are very clearly spirits of the dead, in other words) are indeed born from eggs that are laid by other spirits of the dead. In truth, these pokémon have … interesting reproductive cycles and social structures. Yamask, for example, hatch from eggs, masks and all. Scientists aren’t quite sure how; there are, after all, plenty of mysteries surrounding this world, including and especially what exactly happens when we die. It’s just known that yamask don’t acknowledge their yamask “parents” as their true parents. In fact, yamask tend to be independent after birth, and while they sometimes congregate into groups, they largely begin taking care of themselves after birth, save for a period in which the parent yamask console the newly reborn and help them embrace their new forms.
Phantump, meanwhile, reproduce two ways. The first occurs exactly how you’re told it occurs: when a child dies in the woods, its spirit possesses a stump and becomes a phantump. However, the other way occurs when phantump in general grow old enough to be trained or mature on a mental level. Once a phantump reaches adulthood (in this body, anyway), it becomes capable of mating. As with shuppet and banette, phantump also have the ability to change their bodies and manifest whatever they need to function so long as they remain, ultimately, spirits in a stump. This includes reproductive organs capable of laying eggs. (It’s thought that phantump choose this method of reproduction because they understand that pokémon lay eggs but might not understand … well, how humans do things.)
In other words, it’s very simple, anonymous. Ghost-types reproduce, by and large, by laying eggs just like those laid by any other type of pokémon. Some ghost-types simply need to take a few extra steps before getting to that point.
The Pokédex According to Bill 