Locate an online resource. There are many online resources for learning Arabic, but few are free of charge. Diane Beddoe's personal website includes an overview of Saudi Arabic, a transliteration and definition guide, as well as links to her practice videos on YouTube, all for free. For more information on Diane Beddoe's website, see Resources below.
Engage a "pen pal." Part of learning the language is practicing it; it is impossible to correctly learn Arabic without someone to speak it with. MyLanguageExchange.com (see Resources) is an online website that matches you to a native speaker of Saudi Arabic so that you can practice writing, reading and speaking Arabic, and they can do the same with English.
Listen to and watch Arabic television. Al-Jazeera is based in Qatar which borders Saudi Arabia and, therefore, uses a similar dialect. The al-Jazeera website offers news stories and human interest stories in Arabic as well as English, allowing you to read (or listen to) a story in English and then re-read it in Arabic to increase your understanding.