I have bred them many times and I have given accounts of just how I do it, but have always had someone disagreeing or suggesting alternatives, so if you do feel comfortable with trying my method, it is entirely up to you....
I put both male and female in one tank (24 x 12 x 12")with a glass partition inbetween (1 third space for the male and 2 thirds space on the female's side) so that they can see each other, but hands off....then also, have a second (standby) female in a separate tank, receiving the same conditioning as these 2 do. This is about a week before I intend to spawn them. Only the female side will have a trickle of aeration... none on the male side.
Also on the female side only, there will be plenty planted plants and rocky ornaments to provide ample hiding space. On the male's 1 third area, I'll have a single strand (about 5" long) of hornwort floating plant.
During the week they are separated, I will feed chopped earthworm and bloodworm to condition them both, making sure that every scrap of it is eaten.... remove uneaten foods immediately after 10 minutes. (the temperature is kept at 24/5ish during this week)
On the 2nd/3rd day already, you will notice the male flaring at the glass & she may also show some interrest, and in response, he will start building his nest under the floating hornwort plant.
The night before you intend to breed them, raise your temperature by 1.5 degrees, and then the next morning (Saturday or Sunday) when you have the time to sit down and observe, syphon water out the tank to about 6" depth and remove the partition....
This is where you pull up your chair and observe..... Some vigorous chasing will take place and it is hard not to intervene if it looks like she's loosing the plot, but persevere and if she is well conditioned, she will soon give in... After some time, (may be as much as 4 hours) the intensity of his attacks will subdue and he will hasten back to below his preconstructed nest after each chasing spell... adding a few more bubbles.... If at all they're going to be compatable, it will be during his return visits at the nest that she will follow him there and get herself in a position by his side for him to fold over her and virtually squeeze the eggs from her and they will both sink lower and lower as the eggs also drop to the bottom whilst he sprays his sperm onto them.
When they disengage, he will chase her away again and collect all the milky white eggs in his mouth and place them in the bubble nest... This process may be repeated about 15 to 20 times in around 3 hours and about 8 to 10 eggs are released on every account. When the attacks on her increases in intensity again, it is time to remove her from the tank (very carefully so that you do not desturb the surface breaking his nest)
When the first fry is free swimming,(some 3 days later) you remove the male as well. Siamese fry is probably the smallest fry of all fish & will definitely need infusoria as first food, which should be in the tank already from uneaten bits on the gravel producing the infusoria.
The 2nd (standby) female being conditioned as metioned at the start, is there for in case the males aggression at the introduction to the ist female gets out of hand. That is why careful observation is required during this period.