Enroll in an Arabic course at your local university or community college. Make an appointment with your academic adviser if you're currently enrolled in classes, and if not, with an admissions representative to see about signing up. If you only want to study Arabic without pursuing a degree, you may be able to do so, depending on the policies of the university.
Study abroad in an Arabic-speaking country, such as Jordan, Qatar or Egypt. In addition to the fact that doing so will provide you a teacher who is more than likely a native speaker, it will also fully immerse you into an Arabic-speaking population, giving you ample time to polish and perfect your skills outside of class.
Purchase Arabic-language computer software, such as "Rosetta Stone" or "My Arabic Teacher." Although software can never be a full substitute for a real-life instructor or, better, a full immersion experience, it will familiarize you with the basic grammar, structure and rhythm of the Arabic language.
Meet with an imam (a faithful Muslim who preaches from the Quran) from your local mosque and ask him if he or anyone he knows would be willing to study the Arabic-language Quran with you should you want to study Arabic for primarily religious reasons. Although Islam originates in the Arab world, it's the majority religion of large countries outside of it, including Malaysia and Indonesia -- countries with other official languages. Learning your favorite Quran passages in Arabic won't require you to be fluent in the language, but you may find that you pick up some of its conventions as you study.