The first step is to identify which plants you hope to cross. Do you want to make a new hybrid or just set seed on a particular species?
Some people would rather never see a hybrid, but interesting plants can result. For example, it’s difficult for me to grow both A. warocqueanum and A. papillilaminum in the summer here in South Florida. They just don’t like the heat. However I have a hybrid of the two, originally done by John Banta that grows like gangbusters!
Setting seed among the same species is a great way to increase the diversity. Cuttings are just going to be copies of the plant you started with, but your seedlings will vary a bit. Some are stronger than others, some grow larger, etc.
On an inflorescence the female flowers mature first, followed by the male a little later including pollen production. The inflorescence is ready to accept pollen when tiny droplets of moisture, stigmatic fluid, can be seen on the spadix. This is referred to as anthesis. Often there is even a scent associated with this event. These are pheromones that would normally attract pollinators. In this case, that would be you. First use a paintbrush, your fingers, or collect fresh pollen into a paper towel. Then brush or rub the pollen onto the receptive female flowers. Do this for a couple days in a row if possible. (What the heck, right?). Basically, the biology of it is easy… You need a receptive female spadix AND fresh pollen from another plant. The female flowers are usually only ready for a day or so.
One of the main roadblocks to pollination is not being able to have two inflorescences ready at the same time. It’s a good idea to freeze pollen if there is a specific plant you want to put the pollen on. You can achieve this by using a paintbrush to brush the fresh pollen onto aluminum foil, fold it over, label it and then put the whole thing in a freezer zip lock bag. Make sure you label it with the name of the plant it came from. It’s also a good idea to label the inflorescence you put the pollen on with the pollination information on it. Believe me, you will NOT remember what pollen you slapped on which plant 6 months down the road, especially if you are doing many crosses.
Sometimes very different looking Anthuriums from within the genus can be crossed, but usually plants from different ‘sections’ will not cross… much to my annoyance. I mean, we all need a velvety leaved A. veitchii, right? Obviously there are exceptions.
For some reason I find many of my most mature plants will self pollinate nearly every time they flower. It is impossible to tell if pollen I meticulously applied “took” and will result in a way cool new hybrid, or just selfed again until the resulting seeds are planted and have grown out. If they are eaten by snails or succumb to fungus, you can be assured that your hybrid probably had been a success!
It can take many months for the berries to form before you see if your pollination efforts have been a success. The mature berries can be many different colors depending on the species. Red, purple, orange, red, white, or even green. Usually the color is the same among plants belonging to the same section.