So there is a girl at work who trained me, and I think she is cute and really nice. She was very open with me and I pretty much learned more about her in 1 day than I do with some girls I have known for a year. Anyways she has initiated small talk(as we are working) and I am pretty interested in her. Whenever I talk to her she laughs a lot and plays with her hair when we speak too. So I asked around to some pals and I found that she really hasnt dated but she flirts with me. I also catch her looking over to me sometimes.

So I want to make some more progress and push it more into an actual relationship than flirty friends but I do not want to go right into it and make it awkward at the work place.

I did not get her number yet but she kept asking me when I was going to get a new phone(I broke my old one).

So what do I do?

It's simple, but you're just overcomplicating it. You're too worried, for whatever reason. So RELAX. You probably already know what you should do.
Get her contact info: phone, facebook, whatever.
set up a time and place to see her outside of work. It doesn't have to be elaborate or anything. Try to keep it low-pressure (so not a fancy dinner).
Invite her over to your place. It's always good to have some BS reason for it. Example: hanging out to watch a movie.
Get her alone and let biology take over.

If all you want to do is kiss her and take it slow, you don't need to get her home on the first outing.

You know that trainers are like that, they try to make you feel comfortable at work, so make sure that she's not only trying to be nice if you want to go further.
About the hair thing, i don't see it as an IOI, i just see it as an IOI when they swing with it or when they fix eye contact with you doing it, otherwise can be just a normal thing.
But ok, try your best but don't put yourself into awkward situations, i don't flirt with my work mates because of that, i don't want to lose my job. And there are some cute ones here that i wouldn't mind to have something with them...

But as i usually say: Work is work, pickup is pickup

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