Buy and read "Elements Of Style." To a Virgo, careless grammatical errors are like a 4th-grade violin recital; once they begin, he starts looking for an exit. Don't worry about when to use "farther" versus "further" or "that" versus "which". Rather, focus on mastering "you're" versus "your" and "it's" versus "its". Also, remember that "irregardless" and "definately" aren't words.
Put together at least three well-coordinated outfits. You don't need to be a size 2 to impress Mr. Virgo, so long as you're dressed to the nines. Create a full-body ensemble of complementary colors and textures, including a few tasteful accessories. Each outfit should feel organized and cohesive. Beyond that, just be yourself. Note: if you must wear jeans, make sure that the shoes, jewelry and top tie together strongly. Also, forgo sparkling or reflective accessories in favor of dull metal and natural fibers (wood, stone, fur, leather).
Go easy on the makeup. Smoothing out blemishes and splotches with concealer or foundation is fine. That said, excessive eyeliner and mascara are like tiny Swords of Damocles for Virgo; he'll spend most of the conversation secretly worried that your eyes are about to be hit with a small, painful avalanche of cosmetics.
The Game Plan
Start on a Thursday or Friday. The work week should be winding down, freeing his mind.
Pop a Listerine PocketPaks Fresh Breath Strip (or two). Seriously. Even if he makes some wise-ass comment about how minty your breath smells, deep down he will be in heaven.
Ask him for advice or his opinion on a technical detail. Virgo needs to feel useful. However, he can become extremely indignant if he senses that he's being used. To strike a balance, ask him a question about a detail. For example, instead of asking, "how do you use the printer," say something along the lines of, "I'm trying to print two-sided sheets where the back side is upside down; do you know of any tricks I could try?" In the second case, the question demonstrates that you are a capable person who values efficiency.
Touch his arm or shoulder. Choose a question such that explaining it to Mr. Virgo will require you to casually touch him in some way. Have him pull up a web page on his desktop monitor and rest your hand on his shoulder as you lean over to point out something on screen. Ask him to get something off a high ledge and hold his arm to support him while he's on his tip-toes. Note: the contact must seem natural and platonic; if you give the sense that you're feeling him up, he'll recoil in self-consciousness, wary of prying eyes.
Chat briefly, then return to work. Thank him for his help and strike up a brief conversation. Popular topics include nature, animals, work, philosophy, psychology and pop culture. After a few minutes, wrap the conversation up by saying the two of you should probably get back to work. End the conversation with, "Thanks again for the help."
Repeat on Monday. Note: keep the touching nonchalant and platonic - no fondling!
Repeat on Wednesday. However, instead of ending on "thanks," use an open invitation to a date. For example: "Y'know, I really like talking with you. If you ever want to do something after work, let me know."
Sit back and enjoy your devoted Virgo.