How to get acquainted with a girl you like?

qstoffe
Background:

I've got a huge crush on a girl that I don't really know. She works at the local gym I go to. I usually see her a couple of times a week and we say hi to each other. I make eye contact with her as often as I can. At first we just used to look at each other without expression. Then I tried to smile at her as we made eye contact and she smiled back. I think she knows I like her since I look and glance at her so frequently. I have no idea if she's interested though since she might just be nice to me because she works there.

Since I've seen her so often, talking and training with others around me I almost feel as though I know her. I also attend a group exercise that she leads.

Question is; how do I approach her in a progressive way, bit by bit, to get more acquainted with her? I don't want to come on too strong right away because I think that could make things a bit awkward for us both. I just want to get to know her better and at the same time find out if she's interested in me. To be honest I don't even know if she's single but asking her that might be a little to direct imo.
How to get acquainted with a girl you like?
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