Third, once you decide that you are ready to date, look to God's Word to decide the kind of person to date, and evaluate potential dating partners on those criteria, rather than relying primarily on the world's treatment of ideas like "attraction" and "chemistry." I wrote at some length on this in my article, "Brother, You're Like a Six." For you busy singles with time for only one mildly irritating column per day, the summary is this: Pick a potential dating partner with an eye toward godly manhood and womanhood — with an eye toward who would make a good husband or wife, defined by those characteristics esteems in His Word, not the ones Hollywood likes.
See what an unsatisfying bumper-sticker treatment that was? Among the different roles assigned to men and women in the Bible, men are assigned the role of leadership. This is not a signal of male superiority or of the greater importance of men.
Hilariously, Hollywood even writes these characters into period pieces, as if the normal woman at all levels of society in the 18th and 19th centuries was a post-feminist, post-sexual-revolution, "there-ain't-no-difference-between-me-and-you" libertine. Needless to say, that is not the biblical picture of the responder. Does this mean that a woman should never ask a man out on a first date? Does this mean that a woman shouldn't give the guy the assurance he needs by "leaking" news of her interest to him by way of his friends? He knows what is best for each of us, and all of us must learn to trust Him — especially about things that are really important to us.
Finally, let me advocate the initiating of a relationship under some accountability structure.
But if you're out of college and do not feel specifically called to singleness for biblical reasons, why are you not looking to be married? Albert Mohler has talked about a growing culture in society and in our churches of perpetual boyhood; some psychologists call it the "Peter Pan syndrome." As I said, in the Bible, marriage and family are considered a natural stage of progression toward manhood. Part of your role even at this early stage is to protect the woman of your interest from unnecessary risk and vulnerability by providing a safe context in which she can respond.