Learning to write in Arabic can be a difficult process because the Arabic writing system is so unlike that of English. However, there are a number of good online aids to learning Arabic calligraphy, making this rewarding task a little easier.
Visit searchtruth.com (see Resources) to learn what the letters of the Arabic writing system (called an abjad) look like in different situations. In Arabic, as is true to some extent in other Semitic languages, letters vary in the way you write depending on whether they stand alone or where they're placed within a word. In the case of Arabic, most letters have four forms: stand alone, word initial (first letter), word medial (in the middle of word) and word terminal (last letter of a word). Searchtruth.com outlines all the possible forms of every Arabic letter, and it is important to be able to recognize these forms before learning to write them.
Next, it is important to learn to link letters together when writing. This is because Arabic script joins letters together, never writing them in isolation. I-cias.com (see Resources) provides 4 lessons (lessons 6-9) about how to do this.
If you wish to learn decorative Arabic calligraphy after mastering the writing of the abjad, visit ilovetypography.com (see Resources) to see a number of examples of styles, including Naskher, Thuluth, Diwanii and Tal'iq, with good pictures of the process.
Incorporate your study of Arabic calligraphy into your regular study of the language. Aim for an hour's worth of study every day, especially when you are just beginning. This will bring about quick progress and help keep topics fresh in your mind.