Strike up a conversation with the person you are interested in.
Be bold and don't be afraid to initiate contact. Do not over-analyze your "opening line" -- a classic "hello" should suffice. If you want to prepare for a longer conversation, think of an excuse to speak with the object of your affection beforehand, whether it's about a book he's holding or about the insane weather your city is presently experiencing.
Eye contact is a classic form of flirtation.
Not only is eye contact relatively easy, but it is also subtle. When you speak with someone you like, look directly into her eyes. Keep your gaze locked on her for about three seconds, then look away. This amount of time will get her intrigued.
A sincere and authentic smile is one way to flirt in a casual way.
Flash the man of your dreams a quick smile as you pass him in the hallway. As you smile at him, engaged in the aforementioned eye contact and then look away. Make your smile as genuine as possible, because you do not want to give off a forced appearance. A genuine smile makes you come across as significantly more approachable.
A highly effective flirting tool is praise.
Compliment the woman you covet and try to make her feel special. Be sure that your compliment is genuine and in good taste. Tell her that you think the sound of her speaking voice is musical, or perhaps that you truly admire her sense of style.
Joking around and having a sense of humor is a highly effective flirting technique.
A lot of flirting involves well-meaning teasing -- just be sure not to get personal. Make playful jokes about his adoration for corny 1980s teenage flicks or about her penchant for weird food combinations. Be lighthearted and have some fun.