That's a legitimate question and something I've thought about - how do you know if she is the one??
In Genesis when God brings Eve to Adam for the first time, Adam somehow KNEW she was taken from him.
The passage says:
"This at last is bone of my bones
and flesh of my flesh;
she shall be called Woman,
because she was taken out of Man."
Genesis 2:23 (ESV)
The real interesting part is what God does right after He says it's not good for a man to be alone and He will make Adam a suitable helper. Instead of putting Adam to a deep sleep and make Eve, God brings all the animals to Adam. Interestingly, God doesn't tell or command Adam to name all the animals but rather to see what Adam would name them. As Adam starts to name each animal, I would imagine two things are happening to Adam internally: First, he's running out of names to name animals and feels the need for some help. Second, he's seeing all these animals in a pair, a male and a female, and perhaps thought about himself being alone, wanting his counterpart just like these animals. When, only when Adam was done naming all the animals God brought to him, God put him to a deep sleep and create Eve. I believe God brought those animals to Adam because it would serve some specific purposes like preparing Adam for Eve - perhaps Eve is more appreciated as Adam kept finding himself no suitable helper as it is evidenced in the very first thing he says, "This at last...." Sounds like he was longing for a partner, a suitable helper, someone he can be with in the company, just like those animals in pair. Also, the very first thing Adam does is giving her a name, Eve, which I am sure Adam was very efficient at it by then because of naming all the animals.
What would I say to her, AFTER realizing she is the one?
I don't know.
Maybe, maybe hold her in my arms softly, run through her hair with my hand, and give her a smooch on her left cheek.