Watering the flowers only increases the probability, as the other person has said. Also, using fertilizer will also increase the probability of them breeding.
Oh I should mention that the probability gets spread out across all of the flowers you water. This is why I only buy hybrids in threes so if I wanted to multiply them, I can just water only the three which nearly guarantees me 1-2 new hybrids of the same color tomorrow. If you water other groups, it gets spread out and the chance is generally lowered because there's a hybrid limit per day. If that makes sense haha.
Trying to create a new color of hybrid is different and much harder since the spawn rate of a diff. color is also included which reduces it by quite a bit. That being said, it isn't impossible. I had a huge white flower contraption set up in an attempt to produce purple roses and it ended up being two, lone, unwatered ones next to Fang's house that did. 8'D
disclaimer though this is all from my observations as I've been trying to breed a majority of my own hybrids. iirc I've only bought black lilies instead of breeding from scratch.