Well a good advice is that at least for the first date the guy has to pay unless the man and lady agreed to split the bill before the date. In this age of women empowerment talk and the United Nations millenium development goals well I think it wouldn’t be wrong for the young woman to foot the bill.
It depends on who initiated the date. If I were the one to invite the guy (never happens on a first date), I would pick up the bill without hesitation. If he invited me, however, I would expect him to do the same. In general, it’s my belief that whoever invites, pays. That said, I always make sure I can pay for whatever we are doing too.