While some fish will lay eggs in nests and care for them, not all fish have maternal (or paternal) instincts. Rather than build a nest and defend it, they will simply lay the eggs, fertilize them and then leave them.
This type of breeding means the fry develop rapidly on their own, but it also means that you will need to watch out for them, since their parents won't. In the wild the adult fish would never see their babies again. In the unnatural environment of the fish tank, they are far more likely to eat their young. The adults should be removed immediately after the eggs have been fertilized.
There are two types of breeding where the adults have nothing to do with the eggs: burying and scattering. Tetras, danios and barbs are all fish that tend to scatter their eggs, laying them on rocks, plants and any other surface in the tank. The female will dart about the breeding area laying the eggs while the male will swim after her to fertilize them.
It is fairly rare to have aquarium fish that will bury their eggs, but it does occur. This is the case with grunions, for example; they will dig into the gravel and deposit the eggs there. The male fertilizes them and the eggs are covered again. This is done in the wild to protect against predators and also to protect the eggs when the water dries up. In rare cases, it is necessary for the eggs to dry for a period of time and then be rehydrated in order to hatch.
When breeding these types of fish, whether they bury or scatter their eggs, you will need to move the adults to another tank before the fry hatch. This will ensure plenty of healthy young fish.