Pick your dialect. The Egyptian dialect of Arabic is the most widely understood because most television shows and movies are made in Cairo. People all across North Africa and the Middle East will be able to understand you, even if you have trouble comprehending what they are saying.
Listen to the radio. Tune in to Arabic news radio. News stations are particularly good because if you miss something the first time you hear it, you can pick it up when it is broadcast the next time.
Search the Internet for an interactive audio program. Type "Egyptian Arabic audio" into a search engine and it will take you to the location where you can review a number of options. Find a site that includes audio, so that when you click on the word "shukran" (thank you) you can hear it as well. Keep clicking the audio button until you master the word and then move on to the next.
Download podcasts. Again, keep your target dialect in mind. If you want to be able to talk to your relatives when you visit Abu Dhabi, go with programs from the Gulf States.
Buy or download an audio program that has accompanying print material. As you listen to the words, follow along and try to pronounce then the same way as the presenters.
Listen to Arabic music. There is a wide variety of Arabic music available, from belly dancing to chants from the Quran. Pick the genre that appeals and sing along to your favorite tunes.
Listen to native Arabic speakers every chance you get. Go to the Arabic cultural center and get to know people there. You may even get invited to the Eid al-Fitr feast at the end of Ramadan, which would be an excellent time to practice your Arabic.