biology - How does cross-species (Klingon/Human, Vulcan/Human) breeding work genetically in Star Trek?

While humanoids across the galaxy theoretically share a common remote ancestor, from what I remember each species has evolved convergently towards humanoidness by different routes. So we end up with Humans that have iron based blood vs. Vulcans with copper based blood; Klingons with three lungs and eight chambered hearts, etc for other species. These species all look similar outside, but are very different inside.

Has any episode of any ST series ever attempted to explain how these fairly different genomes can intermix usefully? vs. being a nonstarter like a shark and a dolphin hybrid (similar body design, radically different evolutionary background and genome)?

Answer

Oliver_C's comment is correct.

Starting in "Demons" and Ending in "Terra Prime" we see the failed attempts of human xenophobes to clone a Vulcan Human hybrid. This however is not successful:

Meanwhile, Dr. Phlox scrambles to find a cure for the baby, named Elizabeth (for Tucker's late sister) by T'Pol, who is dying due to defects in the Terra Prime doctors' attempts to reconcile Human and Vulcan DNA. Unfortunately, Phlox is unable to save the girl; the leaders of the soon-to-be-incorporated Coalition of Planets later request to attend her funeral.

In the Enterprise episode "E^2" we meet the alternative timeline captain of the NX-01 Enterprise named Lorian. He is the son of T'Pol and Tucker. He is explained as:

a conception made possible after Doctor Phlox found a way of combining the Vulcan and Human genomes.

This presumably means that the initial incompatibility with the species was overcome. And that Vulcans and Humans wishing to procreate would simply need to see their doctor in order to have success.

This is in contrast to the memory-alpha article on Hybrids, which claims many species are able to interbreed with or without the help of genetic technology. In fact, Humans and Vulcans are quite similar.

Obviously some species are going to be more compatible than others. Bajorians and Cardassians apparently were highly compatible, due to the high number of illegitimate children produced during the occupation of Bajor (I view it unlikely those people sought the assistance of a doctor for procreation).