BlueRose
I stalked the guy's facebook and found that he keeps on writing about her. He even posts love message to her wall. She regularly likes the posts but doesn't reply anything.
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Well...I'm assuming that your reference to "stalk[ing] the guy's facebook" refers to the fact that he has his privacy settings on low and what he puts out there is for all to see? I'm assuming that she is the same way? Is that how you know all this stuff?
Since you both work together, dating a co-worker can be a sticky situation. First of all, does your company have any prohibitions regarding dating co-workers? If I were you, I would check the HR manual to see if they have a policy on this.
Even if it's not prohibited, you still have to tread carefully. If you end up dating, things could go well and eventually you'll get married --- or it could go the other way --- things could go badly.
In this economy, it would be tough to move to another job should things not go well.
Just some food for thought...
Anyway, you don't really say how much you two have talked. If you talk regularly, perhaps you could start by taking your lunch break together---as friends. That way, you can get a feel for what she's really like and she can get a feel for what you're really like. If things go well, then work on developing a friendship before considering taking things to another level.
The last sentence in the above paragraph is contingent on your company's policy on dating co-workers. You must tread carefully as a rule---even more so in this tough economy.