Inbreed? Inbreeding fish is just breeding sister-to-brother or mother-to-son etc...
It happens all the time and has no obvious effect except for when fish are mass in-bred like in the case of neon tetras and dwarf gouramies where it results in a weakened immune system and lots of diseases... Anyone can inbreed a fish and it isn't the slightest bit unusual. Guppies, for example, are in-bred all the time. If you leave the fry your fish produced in the same tank, they'll breed with each other and their parents - that's inbreeding...
Maybe you mean cross-breeding different species? Producing hybrids? That's a little more controversial and a lot more difficult in many cases.
Most cichlids that belong to the same genus will readily inter-breed and produce mixed-species offspring. The same upplies to guppy/molly crosses and platy/swordtail crosses. Many danios will inter-breed too. Gouramies in the trichogaster genus can also apparently inter-breed. You would breed them like any other fish of their species. As they are closely related they will breed together very easily and naturaly.
The reason it is a problem is because some of these fish may end up back in the wild. In some cases, these fish would survive and breed with wild fish. The result would be mixed wild fish which could result in the original species' extinction - similar to what has been happening with dogs inter-breeding with wolves (though they are actualy the same species in this case) or wolves with coyotes - causing a decline in pure individuals of both species.
If you want to try it - well go ahead. Try breeding a male guppy and a female molly. The fry you get will be hybrids. Just make sure you don't sell or give away any of these. Keep them yourself and make sure none end up going down the drain alive...