I have a friend a lot like you. I don't know if she likes me or not. She makes insinuations but we haven't even kissed.
I'm OK with being her friend but sometimes it seems like she wants something more. It's quite irritating.
I in no way am saying that you are irritating. Lol!
Just my situation.

How long have you known this person?
My first thought was if it isn't coming naturally, then maybe it's just not meant to be. Since you are shy, it isn't unusual to take your time getting comfortable.

You've just started going out, so there's a bit of unfamiliarity there.

So get more familiar! Start by touching him! Slide your arm around his lower back when you're walking. Massage his shoulders when you're sitting. If he likes you, he'll dig it. Should break the ice, loosen you both up.

I did this with my Asian honey, and she just MELTED into my touch, like a dying plant in need of a little water. Unfortunately, i couldn't stimulate her too much beyond cuddling.

I agree with bedhog. When you like someone and find them adorable, cute and charming.. it seems like it would just come naturally.

I'm not liking this sentence... "The guy I'm seeing says I'm very closed off" Maybe he is expressing his needs, BUT, I hope that he isn't telling you to change and be something he wants and making you feel there is something wrong with the way you act and you should be somehow different. kwim??

My sister is very shy. She didn't date in high school...too shy. She met her first husband in a college class and she said it all felt so natural to share and for her somehow the shyness wasn't an issue, at least it the marriage. With her second husband it has been much the same, kind of a natural bond that seemed to break down her shyness.
Not saying this isn't the right guy. But sometimes we try too hard to make things work that we kind of fall all over ourselves trying to impress. I guess I'm saying is he really the right guy? And relax and don't worry about the shyness. Ask him questions letting him do the talking and do some of those non verbal messages like one of the previous post suggested.

It may be too soon. How long have you been dating?

I agree, it might be too soon..I too am wondering how long you've been seeing each (there is a big difference between a few weeks, vs a few months, or even years for that mattter).

I've found pre-visualization helps. If you can see in your mind's eye what you'd like to do to/with this guy, you're one step closer to actually doing it. If you can't see yourself doing it, you won't. Maybe the guy doesn't make you feel very touchy-feely, and that's a sign that you need to find a guy who does.