Buy a book with an audio component. Learning the alphabet relies heavily on seeing each letter and hearing the way it sounds. There are multiple letters in Arabic that represent the same letter, so it is important to listen for the subtle differences so that you will better understand them; on the other hand, there are a few letters in Arabic that are not in the English language at all, and these are especially important to hear for the Arabic learner.
Learn the possible connections of each letter. In Arabic, most letters are connected to each other. You will find that each letter has four possibilities: It can be at the beginning of the word, at the end of the word, in the middle of the word or by itself. Each placement is written differently. Knowing how each letter looks in any position is key to being able to write in Arabic.
Pay attention to the sub-vowels. In the Arabic culture, these aids are only seen in children's books and in the Qur'an. The sub-vowels are also used for non-native speakers and act as cues to help people pronounce written words correctly.
Find an Arabic speaker to practice with. He will be able to guide you along, as well as help you differentiate between similar sounding letters.