The Virgo is very discriminating. Virgo has refined tastes, has a kind of built-in elegance of spirit. Virgo is highly intelligent. So the way to attract a Virgo immediately is to appear as if you are a classy person. Virgo is not attracted to anything like a ruffian or a loudmouth or a braggart.
Virgo also appreciates intelligence. In other words, you have something interesting to say. You have interesting opinions. A Virgo doesn't necessarily need a whole lot of attention in the sense of he or she has to be the center of attention. Certainly, a Virgo needs you to listen, to really be in some kind of rapport.
Virgo is also somewhat reserved. It keeps, for a while, its own feelings inside. It's happy to tell you opinions, but feelings are harder to get at. So you need patience and understanding. A Virgo responds very well to a sense that if you can give the Virgo a sense that you are a person of your word, that you are a person of good character, that you are not a lowlife. In general, that immediately will attract a Virgo.
Long-term, a Virgo can be critical and picky. It doesn't mean that the Virgo has turned on you, but simply that the Virgo wants life to be perfect, which it never is. So if you can move through that and see the Virgo's pickiness or criticism not as criticism, but in trying to make things more perfect, make life better, then it's a way of dealing with the Virgo and not being put off by its picky ways.