If you did the asking out, be prepared to pay for the full date (so pick the place/price point accordingly). Take your CC out to pay for the entire meal, say 'dinner's on me'. Next comes a weird social maneuver/mind game wherein your date will often say 'Are you sure? I'd be happy to split', and may or may not mean in. I'd say the safest move, in that case, is to rebut with something along the lines of 'thanks for the offer, but I'd like to treat you', at which point the person will generally thank you and let you pay. If, on the other hand, they really meant the offer, possibly in conjunction with not being into you or really wanting to avoid the feeling of being obligated to you because you paid for the meal, they'll say 'I'd actually feel more comfortable for splitting, but thanks for the generous offer'. Then you split the bill.
I will say that on my first date with my fiance (we were in college - went to a cheap local Chinese restaurant, the total bill could not have been more than $15), I insisted that we split the bill even though he had asked me out. And clearly I like him a whole lot now, enough to marry him. I would have been really unimpressed if he hadn't graciously taken me up on said suggestion to split after I insisted on it (making clear it wasn't just a polite offer). I would have found that really disrespectful - a gentleman offers to pay for a date if he did the asking out, but also should be willing to split the bill if the lady prefers it that way.