Well,I don't really know where to post it so i'll just do it here.
My few relationships that I've had,they 'just happened',I mean,one second we're sitting near each other and the other second we kiss. I didn't really had to talk about 'my feelings' towards her before we become in relationship.
But now there's a new girl,we know each other and I feel there is a connection,but the problem is she's shy a little bit. She's not the type that will talk to anyone and tell him about her feelings (that's what I heard from my friend that got it from her friends) and she's not the type who would just go for the kiss (maybe it's because she's shy or she's afraid of getting rejected). I've been told that she likes me but she wasn't the one who told me that.
What kind of step should I take to get her? Although there is a connection,this is a situation where relationship doesn't come 'just like that' (like my past relationships).

invite her out and, close the gap and kiss her.

Game her like you'd game any other girl, just take it easy on the negs and don't be afraid to send subtle IOI's.