Decide if you want to learn classical Arabic or the more modern standard version. Classical Arabic is the way to go if you are studying for religious purposes. You can also easily pick up the more formal standard version as you progress in the language. If you want to learn Arabic for conversational reasons, learn the modern version. Then you can learn a local dialect that is more informal if you want to at a later time. (See References.)
Learn the Arabic alphabet and the different forms of the letters. According to Al-Bab.com, "If you learn three letters each day and practise for an hour every evening it will take less than two weeks. Practice writing each letter in all its forms (initial, medial and final), pronouncing it aloud as you write. After you have learned a few letters, practice writing them in groups of three, in the order they occur in the alphabet. Each time you write a group, drop the first letter from the beginning and add another to the end, working through the alphabet: alif-ba-ta, ba-ta-tha, ta-tha-jim, tha-jim-ha, etc. Do this once saying the names of the letters, and once pronouncing them as if they were a word: abata, batatha, tathaja, thajaha, etc."
This practice in learning the alphabet will prepare you to read Arabic from the very beginning. You will not have problems learning Arabic words from transliterations, which can cause problems for you later in your studies.
Work through free online lessons in Arabic such as those found at Learn Arabic Online. You will learn basic words, phrases and beginning grammar, and you will begin to build your vocabulary in Arabic. Also utilize lessons for Arabic learners on YouTube. Search for "learn Arabic." You will be able to see the language written and hear it spoken on many of these videos.
You can purchase Arabic lessons through many websites, such as Learn Arabic Online, if you want to learn Arabic on your own. There are also print self-taught Arabic courses available on line, in bookstores, and at your public library.
Join an Arabic language class. There may be some informal classes available in your community. Some universities offer degrees in Arabic, and many of them require students to spend a year in an Arabic-speaking country. The criticism of these degree programs is that the emphasis is placed on literature and history and not as much on learning to speak the language. (See Reference 2.)
You could also spend time in an Arabic-speaking country to learn the language. A list of language courses is available at the Al-Bab website (see Resources).
You can also hire an Arabic tutor either on line or to give you lessons in person. The tutor will be able to help you progress in learning Arabic beyond the basics. You can delve into more Arabic literature and grammar.
Another option is to join an online language exchange such as My Language Exchange. You will meet with an Arabic-speaking student on line who wants to learn English. You can improve your conversational and writing skills by meeting with your partner on line and exchanging e-mails in Arabic.