Ideally the fish should be bred in a gravel free tank with no filters or pumps. A half filled ten gallon tank would be great. If you want to use plants as a spawning medium then use fine leaved bunches like cabomba or java moss. I use a large bottle brush with the handle removed. It provides a safe haven for the eggs and the fish tend not to go in to egg hunt because the bristles of the bottle brush tend to poke the fish in the head as they go in and they avoid it. You also avoid adding any inadvertent egg and fry predators this way as well, such as snails and hydra.
What I would do is separate the sexes for a week or ten days and feed them well. I would only use one pair of fish. Put the female in the spawning tank in the morning and then wait until bedtime to add the male. As the sun comes up on the following morning they will usually spawn. I would arrange this to happen when you are home to observe. Spawning can typically last a few hours.
Remove the breeders after spawning and you will see lots of clear very tiny eggs on the bare bottom of the tank. Do not add a filter or a light. Just leave the tank to get ambient light from the room. The eggs hatch in 36 hours, give or take. The fry will be tiny and look like small slivers of glass. In 4-5 days they will start to swim and look for food. I have only bred the albino version of the Buenos Aires tetra and I used sifted baby brine shrimp as a first food and they grew nice on these.
Once the fry are eating I would change out a third or so of the tank water once every few days and this will be ample to keep the water quality up. As they grow and get to a quarter inch or so you will want to add a sponge filter.
Good luck, Bill