Download and print out charts of the Arabic alphabet. Printing them out and keeping them for reference will help you to study them any time, not only when you are in front of your computer.
Practice writing Arabic with the correct strokes. Keep a notebook and practice writing the letters of the Arabic alphabet until you have memorized how to do it and can recognize individual letters in words easily.
Pronounce the alphabet correctly. Most charts will have the proper pronunciation on them, but you can also listen to the pronunciation of the Arabic alphabet online. The Shariah Program has charts, explanations and audio files about the Arabic alphabet.
Read in Arabic. Practice with the reading lessons in the Shariah Program or begin reading the Arabic in your Quran. Keep practicing until you are proficient in reading, even if you do not understand all the words.
Learn a little at a time. There is no way you can memorize an entire sura (chapter) at once. Take it slow and steady. Learn individual verses in English first. Then try to learn that same verse in Arabic. The Online Quran Project has the entire Quran online with English and Arabic side-by-side.
Write out the verse you have learned in English in Arabic. Sound it out yourself. Repeat it several times.
Write the verse out on an index card. Write the English on one side and the Arabic on the other. Carry it around with you and practice at various times during the day.
Listen to the Quran in Arabic. There are several sites which have audio files of the suras of the Quran online for free. Quran Online has a media page where you can not only hear individual chapters in Arabic but also see the writing as you hear it, so you can read along. Quran 101 has audio files of the several of the suras available for downloading in Real Audio.
Choose a favorite reciter for regular listening. IslamWay has a page dedicated to different reciters of the Quran. Choose a favorite and listen regularly, while following along in your own Quran.