There is no greater dance in the world than that between people in the dating world -- and trying to find the right way to get a woman interested in dating you exclusively is different for every person. Because there is no silver bullet in making yourself irresistible, no set of guaranteed tips to garner a woman's interest, the key is to be yourself, treat the woman in question respectfully, and put your best foot forward.
Be engaged and interested in the woman you're hoping to woo, as well as communicative in your interests and opinions. This is important because it helps you both immediately discover if you have things in common--or if you cannot stand to talk to each other. While physical attraction is always a factor in these things, if you do not have compatible interests there is likely not much hope for a relationship.
Even if you have common interests, there still may not be a connection for the woman you want to date. Be on the look-out for cues that she may be flirting with you, or at least expressing some interest. Signs of interest include maintaining eye contact, a warm smile, initiating some physical contact, or leaning closer. If a woman seems bored, distracted, or is brushing you off, do not pursue her--your continued advances will be seen are more irritating than endearing.
Be genuine and honest in all your interactions. Part of putting your best foot forward is presenting yourself without feeling like you have to edit your personality. Be confident in who you are--it's what makes you unique from a woman's other potential partners. Likewise, respect the woman's personality by listening to her entirely, and treating her opinions as valuable.
Be clean, presentable, and comfortable. What you are wearing is (for the most part) less important than how you wear it. Wearing clothes that are also clean and fit properly makes you look more put-together. A smile will always make you look more appealing than a scowl.
Grace and Tact
This doesn't just help you get a girlfriend, but it also presents you in a good light if things do not work out. Do not act overly clingy or desperate to please her; such attention from someone she's not dating may make her feel uncomfortable. Understand that not every woman will want to be your girlfriend, even if everything else seemed to be going well--she may not be ready for a relationship, or simply not that into you. Accept rejection gracefully.