The golden rule is that it's not awkward unless you make it awkward. It's 100% NORMAL for a confident, socially aware guy to initiate physical contact with a girl, as long as you're not doing anything stupid like grabbing her tit right away.
As said above, a light touch on the small of the back as you guide a girl through a crowd or a doorway is great. Grab an arm or a hand to emphasize a point. Next step up from there might be putting your arm around her. No, don't look at your arm while you do this. Don't draw attention to it, just be playful with her and when she laughs sling your arm around her like she's your little sister and you're about to give her a noogie. When you've gotten more comfort with the chick, playing with her hair or pretending to wipe a smear off her face are great too.
PROTIP: If you're looking for a 'green light' to kiss close because you're not confident enough at first, "triangular gazing" while playing with her hair should tell you all you need to know. If she's holding eye contact while you switch between looking into her eyes and at her lips, and she's letting you lightly play with her hair during this, you are 100% good to go in for the kiss. I've never been rejected for a kiss when a girl was comfortable with these things. Such is the power of kino!!
One kino example I did the other day that I thought was pretty good was this. When I was leaving class late one night with a group of girls, we were going to get dinner at a 24 hour diner in the city. One of the girls, the one I especially want to bang, had a paper due the next day and couldn't stay out late, although she wanted to. So as we were leaving I playfully grabbed her and acted like I was kidnapping her and stuffing her in the car with the rest of us. "Nope, looks like you're getting an F on your paper, 'cause you're coming with us!!" She's like 5'5 110lbs so it was pretty easy to swing her around a little. It was done very playfully and she was loving it. I want to note that I've only known this girl for about 4 weeks. It wasn't weird or creepy that I was doing this, because I had set up the comfort/attraction properly beforehand and I didn't act like a groper or creeper.
You want to look for fun, lighthearted ways to kino while you're still building comfort. While I was pretending to stuff her in the car, I wasn't trying to cop a creepy feel or anything, but it was effective kino because she was fully in my arms (very intimate position usually reserved for a boyfriend), was powerless, and it also sub communicated that I'm a strong guy that can lift her up and physically dominate her (even though I'm only an inch taller than her - hit that gym fellas, especially fellow manlets).
Hope some of that helped.
