You've already had your first date with her. Its absolutely important that you evaluate what's the impression you left on her.
Did you act just friendly? Did you kino? Did you build up tension? Did you made your intentions clear (even if you met tru dating site), where you Good guy? or where you cocky n Funny? Did she give IOI's....
Many of this things relate to the way the following dates might be. For example, if you left things off too friendly, she might be expecting friendship, thus giving you a harder time to flip the script and turn sexual.
But it is always possible

you just have to remember:
Have a strong, rock-solid frame: You like the girl and you want to K close or even better.. F close her! Remember to act on this. Talk on this, feel this and make her feel it! If she doesn't feel your sexually interested in her, she might start seeing you as her a sexual friend who's nice to hang out with... Want that? Ok, so keep your frame. She's the participant, shes the target, not you.
Talk: talk what you need to, if you don't she might not either and things will die. Practice talking,and if not possible for you to hold the conversation, move to some kino. TRY, there are many ways..
Relax: Be confortable with yourself man. Many awkwardness problems come from men not feeling good with themselves. Feeling insecure is a bitch, but you can relax, loosen yourself and not give a fuck about consequences...
Have a confident touch: Touching a woman is not rape. Do not be afraid of the outcome of being touchy. She might like it more than you think, and If she doesn't maybe, just maybe, its not the right time. (but the right time may come later) Be a man that's sure of his touch, do not hesitate, do not let your hand shake or she'll feel you as insecure. Theres no problem with giving hugs, or letting her hug you. Use a gambit to get hugd or to hug her, moxy!
Note: If you become too persistant and shes not into your touch, you may find yourself facing justice in no time. IF she does say NO its NO then. Learn to know when she Means NO.
Do not hesitate when you feel it's time: If you feel tension enough for K close and the vibe is right, do not hesitate for one second, do not be afraid of rejection. SHe might like it, she might not (learned this the hard way and got this same advice).
There's usually a perfect momento for K close, you have to know it and take it.
Call her 2 o 3 days after 1st date, I usually do around 4pm (after lunch, work break-time, after school, etc... Think that is a good time personally) I wouldnt call her the following day. When you call her, just talk to her, like on a normal conversation. Do not rush to invite her for next date (unless shes bussy and cannot talk much on the phone, do invite her).. Keep things light, talk like a renewed person you are. Let her know that she Can have a good time. If she cant make it or doesnt want to do not worry, there are other fish in the sea.
All this is advice that I've been given cuz I've had a situation in which I fucked up. Im just passin on the advice that I personally think applies in your situation. At the same time, re-reading and posting those bits of info, i feel like Im helping myself
Good luck