Any time you meet a girl you're attracted to, you're going to want to hold her hand. You'll need to at some point just to get things going physically, but holding hands is usually the first hurdle.
It can be a big deal (when you haven't yet crossed the barrier) just because it's the bridge that connects you two physically, that makes it clear to you both you're more than just friends.
There's two basic situations for approaching this. The first is holding hands on the initial pick up, and the second is doing so on the first date, or second, however long it takes you.
Situation 1: Holding Hands from the Start, the Pick Up
Escalating physically on the initial pick up usually depends on the environment, but the first situation just comes down to whether you've established a physical rapport. It's less common to do this during the day, but if you meet her at a club or bar, it'll be easier to do this from the start without her giving you much shit. You should do this pretty quickly by holding her hand from the initial conversation, or lightly palming some part of her hand or lower arm, especially at a club. As you start talking to her, you can take her hand and hold it there, and your conversation should have a lot more zing. It just shows you have a lot of confidence, and it'll be easier for you spice things up and banter with her, because there won't be any of that nonsense about "when should I make the first move," or "will it be weird to take her hand now, since I haven't touched her at all yet and she might not be down since it would be so abrupt," because both of you will know why you're there, and both of you will know you're both down, at least for the time being. From there, keeping it physical should be a lot more seamless. You can move from one hand to both hands, to having your hands on her back or waist, based on the comfort of the interaction.
Unless you take her home that night, the next time you'll deal with this is the first date. If the pick up went really well, where you two were touching physically long enough, if you kissed, or if you at least built a good connection over the phone, it should be pretty easy to take her hand from the moment you see her. You can give her a hello hug, and take her hand, and if she shakes it off, try again later. Or you can give her a relaxed high-five, and gauge her receptivity with how willing she is to leave her hand there. If it seems like she's fine with it, you can keep your hands together and go to the date setting.
Situation 2: Holding Hands for the First Time on the First Date
For a daytime pick up, it's a little harder to hold her hand without her putting up her defenses, because the social norms for meeting people during the day are different than those at a club. If the pick up goes well enough where you feel it makes sense to do it, great, but your best bet usually is to insta-date her, and then afterwards as you walk her out, start off by guiding her with your hand on her upper back, and gauge it from there.
If you weren't able to hold her hand at all on the initial pick up, or if the physical rapport you had at the club fizzled out by the date, you'll need to do the work on the actual date. You can try the "relaxed high-five" test when you first see her, but if she doesn't seem ready, you'll need to work it at the date location or after. Sometimes you can find some opportunities to take her by the hand in conversation like over coffee, especially if she opens up to you about some vulnerability she has, but the surest bet is usually when you're leaving the date setting together. So long as it went well, you can usually take her by the hand, back to your pull spot or to where you're dropping her off at. Once you break that physical barrier, it makes the rest of your time together a lot easier.
Learning when to hold a girl's hand is a lot like learning when to kiss--it requires some practice to hone in on your feel for it. As you date more girls, you can get to a point where it'll be much more obvious to you, and it'll feel a lot more natural.
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